STUDY OF PROBABLITY DISTRIBUTION OF RAINFALL
DATA OF BIHAR
A
MINOR PROJECT
Submitted in partial fulfillment of the
requirement for the award of the degree of
BACHELOR OF TECHNOLOGY
In
CIVIL ENGINEERING
By
SAUMYA SINGH
(17101125037)
KUMAR KESHAV
(17101125036)
VIVEK KUMAR
(17101125046)
KHUSHBU SINHA
(17101125008)
RAVI KUMAR RAVI
(17101125034)
GULSHAN KUMAR
(17101125012)
ASHUTOSH KUMAR
(17101125004)
Under the supervision of
PROF. N.N. JHA
RASHTRAKAVI RAMDHARI SINGH DINAKAR COLLEGE
OF ENGINEERING, BEGUSARAI
(Dept. of science & Technology Govt. of Bihar)
Ulao, Singhaul, Begusarai, Bihar 851134
1
CERTIFICATE
The foregoing project report entitled “PROBABLITY DISTRIBUTION OF RAINFALL
DATA OF BIHAR” prepared by the final year student of the Department of Civil
Engineering: RAVI KUMAR RAVI (17101125034), SAUMYA SINGH (17101125037),
KUMAR KESHAV (17101125036), VIVEK KUMAR (17101125046), KHUSHBU
SINHA(17101125008),ASHUTOSH
KUMAR
(17101125004),
GULSHAN
KUMAR(17101125012) of the academic year (2017-2021) is hereby approved and certified
as a creditable study in the technological subject carried out and presented in a satisfactory
manner to warrant its acceptance as pre-requisite to the degree for which it has been
submitted.
PROF. NITYA NAND JHA
Head of Department
(Assistant professor)
Signature of Internal Examiner
Signature of External Examiner
2
DECLARATION
We hereby declare that this project “PROBABLITY DISTRIBUTION OF
RAINFALL DATA OF BIHAR” contains a literature study and research work by
the undersigned candidates for the fulfillment of the requirements for the degree of
Bachelor of Technology in Civil Engineering. This is a bonafide work carried out by
us and the results embodied in this project report have not been reproduced/copied
from any source. The results embodied in this project report have not been submitted
to any other university or institution for the award of any other degree.
NAME:KUMAR KESHAV
VIVEK KUMAR
KHUSHBU SINHA
RAVI KUMAR RAVI
SAUMYA SINGH
ASHUTOSH KUMAR
GULSHAN KUMAR
DATE:-
SIGNATURE:-
3
ACKNOWLEDGEMENT
We would like to express our special thanks of gratitude to our professor “PROF. N. N. JHA”
who gave us golden opportunity to do this wonderful project on the topic "STUDY
PROBABILITY DISTRIBUTION OF RAINFALL DATA OF BIHAR" which helped us in
doing a lot of research and we came to know about so many new things. However it would not
have been possible with the kind support and help of many individuals. We would like to extend
our sincere thanks to all of them.
We are highly indebted to professor "PROF. N N JHA" sir for their guidance and constant
supervision as well as for providing necessary information regarding the project and also for their
support in completing the project. Their constant guidance and willingness to share their vast
knowledge made us understand this project and helped us to complete this project within the
limited time.
We are making this project not only for marks but to also increase our knowledge.
4
ABSTRACT
In India, occurrence and distribution of rainfall is erratic, seasonally variable, and temporal
in nature, which is one of the most important natural input resources for agricultural
production To study the behavior of rainfall variability, the rainfall data of 100 years
(1916–2016) were analyzed for Bihar, India. Hence, frequency analysis is carried out for
best-fit distribution through software for probability density functions viz lognormal, logPearson type III and Gumbel distributions. The expected values are to be compared with
the observed values, and goodness of fit is to be determined by chi-square test Based on
the best-fit probability distribution, the different analysis of rainfall probability at every
200-year return period would be determined. The results of this study would be useful for
agricultural scientists, decision makers, policy planners, and researchers in agricultural
crop planning, canal constructions, and operation management for irrigation and drainage
systems in the semiarid plain region of the Bihar.
5
INDEX
1. INTRODUCTION .................................................................................................... 1
2. LITERATURE REVIEW ............................................................................................. 1
2.1. GENERAL……………………………………………………………………………………………………….2
2.2
PREVIOUS WORK……………………………………………………………………………………………2
2.3
STUDY AREA………………………………………………………………………………………………….6
3. METHODOLOGY .................................................................................................... 9
3.1.1.
ANNUAL RAINFALL ANALYSIS .................................................................... 24
3.1.2.
NORMAL DISTRIBUTION METHOD……………………………………………………….25
3.1.3.
LOG NORMAL DISTRIBUTION METHOD…………………………………………….…26
3.1.4. WEIBULL DISTRIBUTION METHOD .................................................................26
3.1.5.
CHI SQUARE TEST ...................................................................................... 26
4. PROCEDURE ........................................................................................................ 27
5. RESULTS……………..…………………………………………………………………………………………….30
6. FUTURE SCOPE OF WORK…………………………………………………………………………………59
LIST OF FIGURES………………………………………………………..……………………………………………….
LIST OF TABLES………………………………………………………………………………………………………………
6
7
CHAPTER 1
INTRODUCTION
A probability distribution is a statistical function that describes all the possible
values and likelihoods that a random variable can take within a given range.
Establishing a probability distribution that provides a good fit to the monthly
average precipitation across years has long been a topic of interest in the fields of
hydrology, meteorology, agriculture, and others. Rainfall is the main source of
precipitation and study of precipitation provides us knowledge about rainfall. The
analysis of rainfall data strongly depends on its distribution pattern. The main
objective of the current study is to determine the best fit probability distribution for
the average precipitation data of selected stations in Bihar. The probability
distribution function such as normal, Log- normal and weibull were identified on
the basis of several studies conducted on rainfall analysis. The best fit probability
distribution was identified based on the minimum deviation between actual and
estimated values.
This analysis will provide useful information for water resources planners, farmers
and urban engineers to assess the availability of water and create the storage
accordingly. Frequency of probability distribution helps to relate the magnitude of
the extreme events like floods, droughts and severe storms with number of
occurrences such that their chance of occurrence with time can be predicted easily.
8
CHAPTER 2
LITERATURE REVIEW
2.1 General
A brief review is covered in this section about frequency analysis in various
studies of watersheds. A detailed statistical analysis of annual rainfall for Bihar
was carried out using 146 years daily rainfall data.
Probability analysis of annual rainfall series was carried out by employing four
probability distributions namely Normal, Log Normal and Weibull distributions.
Goodness of fit of these distributions was tested by Chi- square test... The
probability distributions namely Log Normal, and Log Pearson Type-III
distribution had been used to).
2.2 PREVIOUS WORK
Alam,. et. al. (2017) The main goal of this paper was to identify the best-fit
probability distribution for every station in Bangladesh which yields the
maximum monthly rainfall for return periods of 10, 25, 50 and 100 years. These
estimates can provide useful guidance for policy making and decision purposes.
Knowing the return period of extreme and catastrophic events can be used in
determining the risk level of damage by extreme events e.g., rainfall, floods etc.
Kalita..et. al. ( April 2017)
10
The expected ADMR and ADMD for different probability distributions such as
Gumbel, Log-Pearson Type-III and Log-normal were calculated for different return
periods. Log-Pearson Type-III distribution gave the lowest calculated chi-square value
for ADMR and Log Normal distribution gave the lowest chi-square value for ADMD
among the probability distribution. Regression models for ADMR and ADMD were
developed by using Weibull's method to predict the rainfall and discharge for different
return period .The trend analysis for prediction of one day maximum rainfall and
discharge for different return period was carried out and it is found that the polynomial
trend line gave better coefficient of determination (R2 ) = 0.992 for ADMR and (R2
)=0.942 for ADMD. This study helps for prediction of ADMR and ADMD to design
hydraulic structure.
Arvind.. et. al. (2017)
From the Rainfall Probability analysis on the Annual and Monthly rainfall for Musiri
Region, it is evident that Gumbel Distribution (Extreme Value Type – I) is ascertained
as the best fit distribution type considering its Least Chi-Square Value among all other
methods of analysis. Chegodayev Distribution from Plotting Position methods is found
to best fit the Annual rainfall data. The present statistical analysis
provides clear picture on rainfall data and it is found that rainfall available in the region
is insufficient to carry out wet crop. Conjunctive use of surface water, available rainfall
and ground water is essential for better agricultural and irrigation management for this
area, Thus, the analysis helps in understanding the rainfall pattern of Musiri region and
also in efficient crop planning and water availability of the region.
Márcio..et. al. ( 09/05/2018)
The study of monthly rainfall probabilities is of great importance due to the increasing
occurrences of extreme events in different regions of Brazil. However, the rainfall
distribution at the southwest region of Paraná State, Brazil, is still unknown. Thus, the
10
aim of this work is to assess the probabilistic distribution of rainfall frequency at Dois
Vizinhos, in the southwest of Paraná State, Brazil. A probabilistic analysis was
performed using a historic 40-year rainfall dataset (1973-2012). The gamma, Weibull,
normal log, and normal probability distributions were compared. The distribution
adherence was performed through Akaike Information Criterion, and the R statistical
software was used for estimation. The results showed that the gamma and Weibull
distributions were most suitable for probabilistic fitting. Based on this, the average
annual rainfall for Dois Vizinhos (PR) was found to be 2,010.6 mm. Moreover, we
found that throughout the year, October has the highest rainfall occurrence probability,
with an 86% rainfall probability of above 150 mm and 64% rainfall probability above
200 mm.
10
2.3 STUDY AREA
Fig.2.3.1
10
The state Bihar is in the eastern part of India. It covers an area of 94,163 square kms
bounded by 24º20’N to 27º31’N latitude and 83º20’E to 88º18’E longitude. It is an
entirely land-locked state, having an average elevation of about 150 meters above mean
sea level. The state shares its boundary with Nepal to the north, the states of West
Bengal to the east, Jharkhand to the south and Uttar Pradesh to the west.
Topographically, Bihar state can be divided into three regions:
 The Sub-Himalayan foot
hills
 The Indo Gangetic Plain
 The
Southern
Plateau
region
The Sub-Himalayan foot hills region lies in the northern part of the state. There
are some small hills like Someshwar and the Dun hills, in the extreme north
of West Champaran district. These hills are offshoots of the Himalayan
system. South of it liesthe Tarai region, a belt of marshy and sparsely
populated region.
Daily Rainfall data from 1870 to 2016 is considered for analysis of trend,
variability and mean rainfall patterns. From the daily rainfall data monthly
rainfall series of each stations are computed and then monthly district
rainfall series has been constructed by considering arithmetic average of all
the station rainfall values within the district. The monthly rainfall series of
the state has been computed by using area weighted rainfall values of all
the districts within the state.
The objective of the analysis is to:
 Identify the spatial pattern of the mean rainfall.
 Understand district wise observed rainfall trend and variability in
annual and SW monsoon season (June, July, august and September)
 To identify the spatial pattern of intensities of various rainfall
events and dry days and also trends if any in the intensity of various
rainfall events and also number of dry days. The analysis has been done
in two parts. For identification of the spatial pattern, mean rainfall and
variability and observed trends, we have used district rainfall series and
results have been brought out for four southwest monsoon months viz.
10
June, July, August, September, for the southwest monsoon season and
for annual. Fig.1 gives the location of the districts of the state. For
identification of mean pattern and also trends of intensities of various
rainfall events we used the station daily rainfall data.
 From the mean and standard deviation, coefficient of variation (CV)
is calculated as follows:
Coefficient of variation (CV) =
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
𝑀𝑒𝑎𝑛
∗ 100
CHAPTER 3
METHODOLOGY
3.1 Methodology
The methodology adopted in this study is Rainfall Statistics, Probability
analysis using plotting position and probabilistic methods. From the
Preliminary study and analysis, variation in results among the plotting
position methods is found to be insignificant.
10
Table 3.1.1 Formulae for Statistical Parameters
Description
Arithmetic Mean
Symbol
Formula
𝑋𝑎𝑣𝑔
Explanation
X is the rainfall
magnitude in mm,
i=1, 2, to n and n is
the length of the
sample.
∑ 𝑋𝑖/𝑛
2
Standard deviation
Co-efficient of variation
Co-efficient of
Skewness
∑
𝐶𝑣
[∑(𝑋𝑖 − 𝑋𝑎𝑣𝑔 ) /(𝑛
1/2
− 1)]
100𝑥(𝜎 − 𝑋𝑎𝑣𝑔 )
𝐶𝑠
(1/𝜎 3 )/
X is the rainfall
magnitude in mm,
i=1, 2, to n and n is
the length of the
sample.
X is the Mean o is
the Standard
deviation
𝜎 is the Standard
deviation
N= Total no. of
years
𝑋𝑎𝑣𝑔 is the Mean
𝑋is the rainfall
magnitude in mm, i1, 2 to n
3.1.1 ANNUAL RAINFALL ANALYSIS
The annual rainfall data is analyzed and the variation in distribution over the
area is studied with the statistical parameters. The best fit distribution method is
found using various plotting position and probabilistic methods.
10
S. No.
Plotting position methods
Probabilistic methods
1
California = m/N
Normal Distribution
2
Hazen = (m-0.5)/N
Log-Normal Distribution
3
Weibull = m/(N+1)
Pearson Type-III Distribution
4
Beard = (m-0.31/(N+0.38)
5
Chegodayev = (m-0.3)/(N+0.4)
Log-Pearson Type-III
Distribution
6
Blom = (m-3/8)(N+1/4)
7
Tukey = (3m-1)/(3N+1)
8
Gringorten = (m-0.44)/(N+0.12)
9
Cunnane = (m-0.4)/(N+0.2)
10
Adamowski = (m-1/4)/(N+1/2)
Extreme Value Type-I
Distribution
Table 3.1.2 Different methods of probability distribution
From the Preliminary study and analysis, variation in results among the plotting
position methods is found to be insignificant and hence, only Weibull method is
adopted for the analysis among them. From the Probabilistic methods, Gumbel
and Normal distribution methods are used. The rainfall data are arranged into a
number of intervals with definite ranges. Mean and standard deviation were
found out for the grouped data. Chi-square values are calculated for the above
methods, with the obtained probabilities. The method that gives the least Chisquare value is found to best fit the distribution. Weibull Distribution is a
continuous probability distribution type where in rainfall amounts are assigned
with a rank and the corresponding probabilities are found out using probability
density function:
(X) = m/ ( n+ 1)
Where,
m and n represents the rank and total number of data used in the analysis.
10
3.1.2 NORMAL DISTRIBUTION METHOD
Normal Distribution is a very common continuous probability distribution.
Normal distributions represent real-valued random variables whose distributions
are not known.
B= 0.5[1 +0.196854 |Z|+0.115194 IZI²+ 0.000344 IZI³ + 0.015927 IZI
Z = (X- Xavg) /a, F (Xi) = for< 0 &F (Xi)= 1 – B for Z> 0
The Probability Density function for the Normal Distribution method is as
follows:
(X) = F (X+ 1)-(X)
Where,
Xi is the rainfall at any instant i = 1,2,3 to n
10
LOG NORMAL DISTRIBUTION METHOD
In probability theory, a log-normal (or lognormal) distribution is a continuous
probability distribution of a random variable whose logarithm is normally
distributed. Thus, if the random variable X is log-normally distributed, then Y =
ln(X) has a normal distribution.[1][2][3] Equivalently, if Y has a normal
distribution, then the exponential function of Y, X = exp(Y), has a log-normal
distribution. A random variable which is log-normally distributed takes only
positive real values. It is a convenient and useful model for measurements in
exact and engineering sciences, as well as medicine, economics and other topics
(e.g., energies, concentrations, lengths, financial returns and other metrics).
WEIBULL DISTRIBUTION METHOD
The Weibull Distribution is a continuous probability distribution used
to analyse life data, model failure times and access product reliability.
... It is an extreme value of probability distribution which is frequently
used to model the reliability, survival, wind speeds and other data. The
only reason to use Weibull distribution is because of its flexibility.
Because it can simulate various distributions like normal and
exponential distributions. Weibull’s distribution reliability is measured
with the help of parameters.
CHI - SQUARE TEST
A chi-squared test, also written as χ2 test, is a statistical hypothesis
test that is valid to perform when the test statistic is chi-squared
10
distributed under the null hypothesis, specifically Pearson's chisquared test and variants thereof. Pearson's chi-squared test is used to
determine whether there is a statistically significant difference
between the expected frequencies and the observed frequencies in
one or more categories of a contingency table.
A chi-square test is a statistical test used to compare observed results
with expected results.
Formula
X^2 = ∑(Oi-Ei)^2/(Ei)
CHAPTER 4
PROCEDURE
• The data for a set of 30 years (1871-1900) and 50 years for (1900-1951) and
(1951-2000) and 16 years (2000-2016) for Bihar is taken.
• Monthly rainfall data for the months of June, July, August and September is
being added to get the annual rainfall for that particular year.
• The data set is arranged in ascending order in terms of magnitude.
10
• Then rank is given to on the basis of magnitude of the data set is done.
• Weibull distribution is calculated (rank/ number of data set +1).
• And the parameters for, normal and lognormal distribution is then calculated.
• Using these parameters their cumulative distribution functions are plotted
along with the data points obtained from weibull’s formula.
• Normal plot and log normal plot was drawn .
• Checking the distribution against chi square test for the given data set it is
found that chi square value with significance level 5% and degree of freedom is
118 for 1871-1900 , 198 for 1900-1950 &1951-2000 and
for
2001- 2016.
It is found that the chi square value is much greater then the ∑(Oi-Ei)^2/(Ei) in
all the data set
• Since all the data set is following both normal and lognormal distribution.
• So all data set is to be tested on the basis of Aic and Bic.
• Now AIC and BIC values are calculated for different distributions.
• The distribution having lowest values of AIC and BIC is the distribution
followed by the data-set.
• This is done for 4 separate data-sets.
10
10
CHAPTER 5
RESULTS
RAINFALL DATA OF BIHAR FOR THE MONTH OF JUNE, JULY, AUGUST & SEPTEMBER FROM 1871 TO
2016
YEAR
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
JUNE
2347
1448
1079
3267
2361
1409
448
1304
1691
1789
2822
1957
3454
1785
1095
1737
2377
920
3241
3095
1674
1949
2098
1997
1035
1529
3167
1218
2610
2859
843
1047
1832
2469
429
JULY
3857
3331
3717
2844
2622
2211
3007
2934
3991
4204
2434
1567
2881
2248
3652
4433
2184
3988
3669
5607
2410
3403
4643
3007
3734
2838
2698
2952
5912
3432
2355
3432
1832
3910
3675
AUGUST SEPTEMBER
3807
4173
1880
2307
2546
807
2413
3222
3112
1400
3396
2519
1473
1684
2909
2008
3271
4456
3432
876
3228
1725
3387
1526
2269
1008
1840
1384
3647
3698
4146
3678
2485
1913
4104
1423
2371
2985
3896
2113
2234
961
4698
1183
2206
2846
3645
2689
2904
1755
2116
1342
2848
2126
3621
5362
4295
2308
1842
2891
3589
1532
2318
3775
1832
1832
3720
806
5083
3115
14
TOTAL RAINFALL
14184
8966
8149
11746
9495
9535
6612
9155
13409
10301
10209
8437
9612
7257
12092
13994
8959
10435
12266
14711
7279
11233
11793
11338
9428
7825
10839
13153
15125
11024
8319
10572
7328
10905
12302
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
2186
2506
844
4590
2376
2965
1408
3976
824
1410
2525
2657
2430
2114
1086
1310
3563
1716
1155
1058
427
1208
1766
2141
1713
506
1204
1855
1444
1115
1756
824
3709
2203
1193
1913
1352
1295
1842
958
1766
769
3557
2763
1705
2697
3544
1885
3287
2422
2694
3444
4389
2900
2176
4760
3875
3386
3910
2222
5614
3063
4410
2829
3618
3205
3000
4750
1457
3812
4208
1789
4703
2035
3646
2901
3135
2147
2436
2923
2019
2204
3928
3762
4765
2223
1465
3414
2781
4141
2979
4495
4674
3899
3391
1940
5547
1949
2267
4735
3419
2283
2701
3614
2974
1826
3097
3398
2094
2211
2246
3496
2365
4442
2888
4967
4054
2707
3058
4371
3520
3333
2926
2627
2559
2705
1024
2032
1370
1821
2625
2911
1112
2598
748
1925
2857
2428
2948
2213
3527
3564
2344
1579
3234
2476
1993
1611
1046
1245
2737
2701
2002
1451
2390
3449
3946
1634
2145
2605
2173
1815
3930
1764
2027
2669
2576
2030
11532
9524
5384
12522
11326
11902
8786
13491
8940
10678
13162
9925
13101
11036
10755
12995
13236
7800
12704
10211
9804
7474
9527
9989
9544
10168
6909
10614
10407
10795
13293
9460
13554
10416
9559
10246
11238
9315
8814
8458
10829
9266
15
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1057
2120
3287
1225
3187
2214
1546
1420
3073
1248
1108
1066
820
2288
1458
1531
1264
835
1013
695
3103
2133
2083
2869
355
1994
1421
1055
1432
1063
2069
860
1724
939
2045
1116
4105
1567
1656
1617
1639
1720
4005
4784
2528
3693
2296
3899
3472
4423
1728
3821
1870
2383
2955
2214
2074
3174
4877
2860
1895
2683
3074
3135
3324
3243
1526
2254
4948
3624
2210
5308
2915
4636
4019
5570
2234
3406
5061
5035
4219
4728
2811
4251
3294
3648
2873
1967
3173
2729
3035
2793
2746
3856
3940
2653
2888
2655
3772
2950
1506
3410
2420
2563
2193
3634
2490
4207
1908
2243
3072
1366
2875
2445
2702
1662
3529
2879
7527
2359
3181
2411
2196
5949
4153
1549
2931
2305
1320
1020
3298
3208
1182
2149
3823
1277
1972
1170
3642
1578
2379
2656
2321
2419
1110
2078
952
2641
3656
1431
2628
3132
2564
2897
4095
1057
2184
1036
1878
1737
1408
2070
2668
2384
1913
3551
1685
3279
11287
12857
10008
7905
11954
12050
9235
10785
11370
10202
8890
7272
10305
8735
9683
10311
9968
9524
6438
8019
9322
11543
11553
11750
6417
9623
12005
8942
10612
9873
9870
8194
11150
11125
13214
8951
15015
11397
9984
15845
10288
10799
16
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
1494
2141
1027
1618
1260
1447
2708
2671
834
2868
2809
1759
910
2761
2211
992
2527
1542
3158
741
941
2744
917
2130
1322
1315
1367
4395
1746
3208
2103
2122
3111
2509
5124
4749
4253
3024
1819
3156
2942
3976
2782
3063
4978
3876
1953
2977
2339
3315
1624
2666
2218
3417
1892
3420
2346
3779
3713
3225
4170
3264
3745
3234
1881
1511
2171
2829
2180
3333
1733
3243
3083
3075
2019
3695
2345
2084
3008
2995
1566
1583
2620
1008
3559
2331
3076
2022
2292
2288
1714
3422
2246
1515
1332
1002
1286
3252
3436
1680
2087
1559
3040
1698
1628
1613
1023
3602
9364
9927
7589
11059
9426
10859
11409
13351
11616
12069
11136
7335
7752
9864
9369
8393
10575
13199
11797
7856
7496
11818
8275
7466
8609
7551
9952
Analysis of rainfall data of Year 1871 – 1900 is below.
17
Increasing
Order
Rainfall
Rank
448
1
807
2
876
3
920
4
961
5
1008
6
1035
7
1079
8
1095
9
1183
10
1218
11
1304
12
1342
13
1384
14
1400
15
1409
16
1423
17
1448
18
1473
19
1526
20
1529
21
1567
22
1674
23
1684
24
1691
25
1725
26
1737
27
1755
28
1785
29
1789
30
1840
31
1842
32
1880
33
1913
34
1949
35
1957
36
1997
37
2008
38
Weibull
Distribution
0.008264463
0.016528926
0.024793388
0.033057851
0.041322314
0.049586777
0.05785124
0.066115702
0.074380165
0.082644628
0.090909091
0.099173554
0.107438017
0.115702479
0.123966942
0.132231405
0.140495868
0.148760331
0.157024793
0.165289256
0.173553719
0.181818182
0.190082645
0.198347107
0.20661157
0.214876033
0.223140496
0.231404959
0.239669421
0.247933884
0.256198347
0.26446281
0.272727273
0.280991736
0.289256198
0.297520661
0.305785124
0.314049587
ln Rainfall
6.1047932
6.6933237
6.7753661
6.8243737
6.8679744
6.9157234
6.9421567
6.98379
6.9985096
7.0758089
7.1049654
7.1731917
7.2019163
7.2327331
7.2442275
7.2506355
7.2605226
7.2779386
7.2950564
7.3304052
7.3323692
7.3569182
7.4229713
7.4289272
7.4330753
7.4529823
7.4599148
7.4702241
7.4871737
7.4894121
7.5175209
7.5186072
7.5390271
7.556428
7.5750717
7.579168
7.5994013
7.6048945
Normal Cdf
0.02092523
0.04419681
0.05047131
0.05482992
0.05915418
0.06443539
0.06763089
0.0730989
0.07516906
0.08736133
0.09260097
0.10645608
0.11303321
0.1206344
0.12362269
0.12532619
0.12800855
0.13289711
0.1379127
0.14896832
0.14961134
0.15791643
0.18289638
0.18535073
0.18708089
0.19562579
0.19869734
0.20335882
0.21127139
0.21233986
0.22623715
0.22679242
0.23748739
0.24699532
0.25759549
0.25998276
0.27208794
0.27546532
18
Log. Norm
Cdf
0.000120276
0.008427479
0.013514213
0.017674746
0.022250692
0.028370266
0.032321939
0.039458501
0.042269654
0.059792352
0.067719332
0.089418147
0.09996286
0.112255289
0.11710616
0.119874068
0.124234685
0.132183209
0.140330695
0.15821556
0.159251295
0.172571109
0.211814534
0.21559276
0.218247124
0.231244478
0.235870074
0.242842222
0.254543378
0.256110438
0.276208677
0.277000711
0.292091418
0.305245391
0.319623061
0.322819703
0.338798283
0.343188394
(C-E)2
0.0001603
0.0007655
0.0006594
0.000474
0.000318
0.0002205
9.564E-05
4.877E-05
6.223E-07
2.225E-05
2.862E-06
5.304E-05
3.131E-05
2.432E-05
1.185E-07
4.768E-05
0.0001559
0.0002516
0.0003653
0.0002664
0.0005732
0.0005713
5.164E-05
0.0001689
0.0003814
0.0003706
0.0005975
0.0007866
0.0008064
0.0012669
0.0008977
0.0014191
0.0012418
0.0011558
0.0010024
0.0014091
0.0011355
0.0014887
(C-F)2
6.63278E-05
6.56334E-05
0.00012722
0.00023664
0.000363727
0.00045014
0.000651745
0.000710606
0.001031085
0.000522227
0.000537765
9.5168E-05
5.5878E-05
1.18831E-05
4.70703E-05
0.000152704
0.000264426
0.000274801
0.000278693
5.00372E-05
0.000204559
8.55084E-05
0.000472275
0.000297413
0.000135386
0.000267926
0.000162042
0.000130811
0.000221235
6.6856E-05
0.000400413
0.000157199
0.00037497
0.00058824
0.000922146
0.000640042
0.001089869
0.00084907
2098
2113
2116
2126
2184
2206
2211
2234
2248
2269
2307
2308
2347
2361
2371
2377
2410
2413
2434
2485
2519
2546
2610
2622
2689
2698
2822
2838
2844
2846
2848
2859
2881
2891
2904
2909
2934
2952
2985
3007
3007
3095
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
0.32231405
0.330578512
0.338842975
0.347107438
0.355371901
0.363636364
0.371900826
0.380165289
0.388429752
0.396694215
0.404958678
0.41322314
0.421487603
0.429752066
0.438016529
0.446280992
0.454545455
0.462809917
0.47107438
0.479338843
0.487603306
0.495867769
0.504132231
0.512396694
0.520661157
0.52892562
0.537190083
0.545454545
0.553719008
0.561983471
0.570247934
0.578512397
0.58677686
0.595041322
0.603305785
0.611570248
0.619834711
0.628099174
0.636363636
0.644628099
0.652892562
0.661157025
7.6487398
7.655864
7.6572828
7.6619976
7.6889133
7.6989362
7.7012002
7.711549
7.7177962
7.7270945
7.7437033
7.7441366
7.7608932
7.7668405
7.7710671
7.7735945
7.787382
7.7886261
7.7972913
7.8180279
7.8316173
7.8422788
7.8671055
7.8716927
7.8969247
7.900266
7.9452011
7.9508549
7.9529668
7.9536698
7.9543723
7.9582272
7.9658927
7.9693577
7.9738444
7.9755647
7.984122
7.9902382
8.001355
8.0086982
8.0086982
8.0375432
0.30384703
0.30870136
0.30967628
0.31293569
0.33212306
0.33952135
0.34121157
0.34902723
0.35381639
0.3610435
0.37424646
0.37459598
0.38830518
0.39326158
0.39681255
0.39894726
0.41074063
0.41181694
0.41936926
0.43782934
0.45021427
0.46008464
0.48356844
0.48798049
0.51262627
0.51593529
0.56131646
0.56712646
0.56930155
0.57002611
0.57075044
0.57472993
0.58266572
0.586262
0.59092632
0.59271691
0.60164009
0.60803233
0.61967486
0.62737747
0.62737747
0.65765419
19
0.378946364
0.384865295
0.386047298
0.389982788
0.412654722
0.421176724
0.423106963
0.431953044
0.437309994
0.445304222
0.459637075
0.460011845
0.474526676
0.479687515
0.483357248
0.48555236
0.497533269
0.498614566
0.50614606
0.524155691
0.535933504
0.545152302
0.566517119
0.570445345
0.591918224
0.594742679
0.632191887
0.636823994
0.638549226
0.639122872
0.639695803
0.642834136
0.649045929
0.651840905
0.655447719
0.656826939
0.663656362
0.66850489
0.677245194
0.682965685
0.682965685
0.705006182
0.000341
0.0004786
0.0008507
0.0011677
0.0005405
0.0005815
0.0009418
0.0009696
0.0011981
0.001271
0.0009432
0.0014921
0.0011011
0.0013316
0.0016978
0.0022405
0.0019189
0.0026003
0.0026734
0.001723
0.0013979
0.0012804
0.0004229
0.0005962
6.456E-05
0.0001687
0.0005821
0.0004697
0.0002428
6.468E-05
2.525E-07
1.431E-05
1.69E-05
7.708E-05
0.0001533
0.0003554
0.000331
0.0004027
0.0002785
0.0002976
0.000651
1.227E-05
0.003207219
0.002947055
0.002228248
0.001838296
0.003281322
0.003310893
0.002622068
0.002681972
0.002389278
0.002362933
0.002989727
0.002189183
0.002813143
0.002493549
0.002055781
0.00154224
0.001847952
0.001281973
0.001230023
0.00200855
0.002335808
0.002428965
0.003891874
0.003369646
0.00507757
0.004331885
0.009025343
0.008348376
0.007196166
0.005950487
0.004823007
0.004137286
0.003877437
0.003226193
0.002718781
0.002048168
0.001920337
0.001632622
0.001671302
0.00146977
0.000904393
0.001922749
3112
3167
3222
3228
3241
3267
3271
3331
3387
3396
3403
3432
3432
3454
3621
3645
3647
3652
3669
3678
3698
3717
3734
3807
3857
3896
3988
3991
4104
4146
4173
4204
4295
4433
4456
4643
4698
5362
5607
5912
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
0.669421488
0.67768595
0.685950413
0.694214876
0.702479339
0.710743802
0.719008264
0.727272727
0.73553719
0.743801653
0.752066116
0.760330579
0.768595041
0.776859504
0.785123967
0.79338843
0.801652893
0.809917355
0.818181818
0.826446281
0.834710744
0.842975207
0.851239669
0.859504132
0.867768595
0.876033058
0.884297521
0.892561983
0.900826446
0.909090909
0.917355372
0.925619835
0.933884298
0.94214876
0.950413223
0.958677686
0.966942149
0.975206612
0.983471074
0.991735537
8.0430209
8.06054
8.0777576
8.079618
8.0836372
8.0916274
8.092851
8.1110278
8.1276999
8.1303535
8.1324127
8.1408985
8.1408985
8.1472883
8.1945055
8.2011116
8.2016602
8.2030302
8.2076744
8.2101244
8.2155474
8.2206722
8.2252353
8.2445968
8.257645
8.2677057
8.2910451
8.2917971
8.3197174
8.3298993
8.3363905
8.3437917
8.3652068
8.3968318
8.4020068
8.443116
8.4548922
8.5870923
8.6317711
8.6847395
0.6633951
0.68170363
0.69957873
0.70150102
0.70564665
0.71385715
0.71511059
0.73359081
0.75027421
0.75290276
0.75493692
0.76326731
0.76326731
0.76948156
0.81357527
0.81945274
0.81993723
0.82114487
0.82521261
0.82734215
0.83201495
0.83637799
0.84021882
0.85603611
0.86623933
0.8738446
0.89057605
0.89109343
0.90931898
0.91548164
0.91927405
0.92346819
0.93482383
0.94949514
0.95166223
0.96664634
0.97024199
0.99373235
0.99676192
0.99866736
20
0.709110651
0.722055352
0.734496905
0.735824186
0.738679934
0.744309752
0.745166273
0.757710925
0.768916196
0.770672677
0.772030441
0.777577895
0.777577895
0.781703817
0.810796352
0.81466733
0.814986534
0.815782286
0.818463834
0.819868557
0.822953549
0.825838005
0.828381076
0.838905782
0.845755907
0.850904165
0.862400921
0.862760988
0.87567597
0.880167216
0.882970073
0.886108833
0.894851505
0.90685797
0.908722101
0.922558457
0.926212532
0.958734075
0.966637699
0.974348052
SUM
3.632E-05
1.614E-05
0.0001857
5.309E-05
1.003E-05
9.693E-06
1.519E-05
3.992E-05
0.0002172
8.283E-05
8.241E-06
8.624E-06
2.838E-05
5.443E-05
0.0008095
0.0006793
0.0003343
0.0001261
4.943E-05
8.026E-07
7.267E-06
4.352E-05
0.0001215
1.203E-05
2.339E-06
4.789E-06
3.942E-05
2.157E-06
7.212E-05
4.084E-05
3.681E-06
4.63E-06
8.827E-07
5.397E-05
1.56E-06
6.35E-05
1.089E-05
0.0003432
0.0001766
4.805E-05
0.0570489
0.00157523
0.001968644
0.002356762
0.001731335
0.001310483
0.001126673
0.000684241
0.000926484
0.001114158
0.000722052
0.000398574
0.00029747
8.06917E-05
2.34674E-05
0.000659071
0.000452792
0.000177786
3.43974E-05
7.95329E-08
4.32665E-05
0.000138232
0.000293684
0.000522515
0.000424292
0.000484558
0.000631461
0.000479461
0.000888099
0.000632546
0.00083658
0.001182349
0.001561119
0.001523559
0.00124544
0.00173815
0.001304599
0.001658902
0.000271344
0.000283363
0.000302325
0.17477554
MEAN
Std. Dev.
CUMULATIVE
2654.7
1084.4
318561
Log Normal Dist.
7.7902197
0.4589802
934.82636
MSE
AIC
BIC
Normal Dist.
0.0004754
-394.7521
-394.5937
Log Normal Dist.
0.001456463
-336.4040713
-338.3248901
1,2
1
0,8
Normal cdf
0,6
Log.Normal Cdf
0,4
0,2
0
0
1000
2000
3000
4000
5000
21
6000
7000
Analysis of rainfall data of Year 1900 - 1950 is below.
Increasing
Order
Rainfall
Rank
427
1
429
2
506
3
748
4
769
5
806
6
824
7
824
8
843
9
844
10
958
11
1024
12
1046
13
1047
14
1057
15
1058
16
1086
17
1112
18
1115
19
1155
20
1193
21
1204
22
1208
23
1245
24
1295
25
1310
26
1320
27
1352
28
1370
29
1408
30
1410
31
1444
32
1451
33
1457
34
1465
35
1532
36
Weibull
Distribution
0.004975124
0.009950249
0.014925373
0.019900498
0.024875622
0.029850746
0.034825871
0.039800995
0.044776119
0.049751244
0.054726368
0.059701493
0.064676617
0.069651741
0.074626866
0.07960199
0.084577114
0.089552239
0.094527363
0.099502488
0.104477612
0.109452736
0.114427861
0.119402985
0.124378109
0.129353234
0.134328358
0.139303483
0.144278607
0.149253731
0.154228856
0.15920398
0.164179104
0.169154229
0.174129353
0.179104478
ln Rainfall
6.056784
6.0614569
6.2265367
6.617403
6.645091
6.6920837
6.7141705
6.7141705
6.736967
6.7381525
6.8648478
6.9314718
6.9527286
6.9536842
6.96319
6.9641356
6.9902565
7.0139155
7.0166097
7.0518556
7.0842264
7.0934046
7.0967214
7.1268908
7.166266
7.1777824
7.185387
7.2093403
7.222566
7.2499255
7.251345
7.2751723
7.2800083
7.2841348
7.2896105
7.3343294
Normal Cdf
0.02397719
0.02407956
0.02830933
0.04578937
0.04764656
0.05106512
0.05279737
0.05279737
0.05467609
0.05477642
0.06719836
0.07532661
0.07819638
0.07832877
0.07966201
0.07979627
0.08362548
0.08730329
0.08773531
0.09364874
0.09953432
0.10128745
0.1019305
0.10801997
0.116659
0.11934375
0.12115763
0.12709202
0.13051762
0.13795766
0.1383571
0.14526823
0.14671946
0.14797108
0.149651
0.16421843
22
Log. Norm
Cdf
0.00026096
0.00027034
0.00089216
0.00993176
0.01152525
0.01473989
0.01649995
0.01649995
0.01850222
0.01861178
0.03395548
0.04550636
0.04979528
0.0499954
0.05202134
0.0522264
0.05814851
0.06395646
0.0646455
0.07419929
0.08389083
0.0868046
0.08787595
0.09807735
0.11266183
0.11720646
0.1202777
0.13032052
0.13610766
0.1486307
0.14930078
0.16084997
0.16326333
0.16534119
0.16812469
0.191975
(C-E)2
0.000361
0.0002
0.000179
0.00067
0.000519
0.00045
0.000323
0.000169
9.8E-05
2.53E-05
0.000156
0.000244
0.000183
7.53E-05
2.54E-05
3.77E-08
9.06E-07
5.06E-06
4.61E-05
3.43E-05
2.44E-05
6.67E-05
0.000156
0.00013
5.96E-05
0.0001
0.000173
0.000149
0.000189
0.000128
0.000252
0.000194
0.000305
0.000449
0.000599
0.000222
(C-F)2
2.2223E-05
9.3701E-05
0.00019693
9.9376E-05
0.00017823
0.00022834
0.00033584
0.00054294
0.00069032
0.00096967
0.00043143
0.0002015
0.00022145
0.00038637
0.00051101
0.00074942
0.00069847
0.00065514
0.00089293
0.00064025
0.00042382
0.00051294
0.000705
0.00045478
0.00013727
0.00014754
0.00019742
8.0694E-05
6.6764E-05
3.8817E-07
2.4286E-05
2.7093E-06
8.3864E-07
1.4539E-05
3.6056E-05
0.00016565
1579
1611
1634
1705
1713
1716
1756
1764
1766
1766
1789
1815
1821
1826
1832
1832
1832
1832
1842
1855
1885
1913
1925
1940
1949
1993
2002
2019
2027
2030
2032
2035
2094
2114
2120
2141
2145
2147
2173
2176
2186
2203
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
0.184079602
0.189054726
0.194029851
0.199004975
0.2039801
0.208955224
0.213930348
0.218905473
0.223880597
0.228855721
0.233830846
0.23880597
0.243781095
0.248756219
0.253731343
0.258706468
0.263681592
0.268656716
0.273631841
0.278606965
0.28358209
0.288557214
0.293532338
0.298507463
0.303482587
0.308457711
0.313432836
0.31840796
0.323383085
0.328358209
0.333333333
0.338308458
0.343283582
0.348258706
0.353233831
0.358208955
0.36318408
0.368159204
0.373134328
0.378109453
0.383084577
0.388059701
7.364547
7.3846104
7.3987863
7.4413204
7.4460015
7.4477513
7.4707938
7.4753392
7.4764724
7.4764724
7.4894121
7.5038407
7.5071411
7.5098831
7.5131635
7.5131635
7.5131635
7.5131635
7.5186072
7.52564
7.5416831
7.556428
7.5626812
7.5704433
7.5750717
7.5973963
7.601902
7.6103576
7.6143121
7.6157911
7.6167758
7.6182511
7.6468314
7.6563372
7.6591714
7.6690283
7.6708948
7.6718268
7.683864
7.6852436
7.6898287
7.6975753
0.17496841
0.18253729
0.1881018
0.20592936
0.20799908
0.20877838
0.21933239
0.2214794
0.22201802
0.22201802
0.22826568
0.23544576
0.23712022
0.23852059
0.24020699
0.24020699
0.24020699
0.24020699
0.24303205
0.24673132
0.2553819
0.26359652
0.26715789
0.2716435
0.27435275
0.28778682
0.2905725
0.2958685
0.29837597
0.29931877
0.29994804
0.30089308
0.31974463
0.32624551
0.32820623
0.33510581
0.33642644
0.33708751
0.34572662
0.34672874
0.35007684
0.35579533
23
0.20920676
0.22113473
0.22979206
0.2568734
0.25995212
0.2611078
0.27656918
0.27967133
0.28044729
0.28044729
0.2893813
0.29949821
0.30183464
0.303782
0.30611913
0.30611913
0.30611913
0.30611913
0.31001484
0.31507945
0.32676255
0.33765249
0.34231293
0.34813132
0.35161799
0.36860656
0.3720679
0.37859152
0.38165452
0.38280195
0.38356653
0.38471284
0.40710745
0.41462768
0.41687609
0.42471642
0.42620456
0.42694798
0.43657234
0.43767794
0.44135574
0.44758091
8.3E-05
4.25E-05
3.51E-05
4.79E-05
1.62E-05
3.13E-08
2.92E-05
6.63E-06
3.47E-06
4.68E-05
3.1E-05
1.13E-05
4.44E-05
0.000105
0.000183
0.000342
0.000551
0.000809
0.000936
0.001016
0.000795
0.000623
0.000696
0.000722
0.000849
0.000427
0.000523
0.000508
0.000625
0.000843
0.001115
0.0014
0.000554
0.000485
0.000626
0.000534
0.000716
0.000965
0.000751
0.000985
0.00109
0.001041
0.00063137
0.00102913
0.00127894
0.00334875
0.00313287
0.00271989
0.00392362
0.00369249
0.00319979
0.00266169
0.00308585
0.00368355
0.00337021
0.00302784
0.00274448
0.00224796
0.00180094
0.00140343
0.00132372
0.00133024
0.00186455
0.00241035
0.00237955
0.00246253
0.00231702
0.00361788
0.00343807
0.00362206
0.00339556
0.00296412
0.00252337
0.00215337
0.00407349
0.00440484
0.00405034
0.00442324
0.00397158
0.00345612
0.00402438
0.0035484
0.00339553
0.00354277
2204
2211
2213
2222
2223
2246
2267
2283
2305
2318
2344
2355
2365
2376
2390
2422
2428
2430
2436
2469
2476
2506
2525
2528
2559
2576
2598
2605
2625
2627
2657
2669
2694
2697
2701
2701
2705
2707
2737
2763
2781
2829
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
0.393034826
0.39800995
0.402985075
0.407960199
0.412935323
0.417910448
0.422885572
0.427860697
0.432835821
0.437810945
0.44278607
0.447761194
0.452736318
0.457711443
0.462686567
0.467661692
0.472636816
0.47761194
0.482587065
0.487562189
0.492537313
0.497512438
0.502487562
0.507462687
0.512437811
0.517412935
0.52238806
0.527363184
0.532338308
0.537313433
0.542288557
0.547263682
0.552238806
0.55721393
0.562189055
0.567164179
0.572139303
0.577114428
0.582089552
0.587064677
0.592039801
0.597014925
7.6980292
7.7012002
7.7021043
7.706163
7.7066129
7.7169061
7.7262127
7.7332456
7.742836
7.74846
7.7596142
7.764296
7.7685333
7.7731737
7.7790486
7.7923489
7.7948232
7.7956465
7.7981126
7.8115685
7.8143996
7.8264431
7.8339963
7.8351838
7.8473718
7.8539931
7.8624972
7.865188
7.8728362
7.8735978
7.8849529
7.8894591
7.8987824
7.8998953
7.9013774
7.9013774
7.9028572
7.9035963
7.9146177
7.9240723
7.9305659
7.9476786
0.35613274
0.35849774
0.35917446
0.36222514
0.36256465
0.37040271
0.37760659
0.38312413
0.39074942
0.39527531
0.40436902
0.40823228
0.4117521
0.41563211
0.42058217
0.43194265
0.43407932
0.43479197
0.4369312
0.44872827
0.45123688
0.4620089
0.46884614
0.46992659
0.48110283
0.4872386
0.4951833
0.49771171
0.50493589
0.50565826
0.51649024
0.52082007
0.52983208
0.53091258
0.5323529
0.5323529
0.5337928
0.53451258
0.54529447
0.55461215
0.56104554
0.57811809
24
0.44794601
0.45049833
0.45122646
0.45449691
0.45485967
0.46316808
0.470694
0.47638849
0.48416114
0.48872227
0.49777207
0.50157126
0.50500959
0.50877456
0.51354005
0.5243204
0.52632413
0.52699079
0.52898703
0.53986509
0.54215034
0.55185518
0.55792624
0.55887945
0.56864291
0.57392984
0.58070061
0.58283806
0.5889
0.58950252
0.59845984
0.60200047
0.60929902
0.61016778
0.61132376
0.61132376
0.61247706
0.6130527
0.62160645
0.62889718
0.63387805
0.64689483
0.001362
0.001561
0.001919
0.002092
0.002537
0.002257
0.00205
0.002001
0.001771
0.001809
0.001476
0.001563
0.00168
0.001771
0.001773
0.001276
0.001487
0.001834
0.002084
0.001508
0.001706
0.001261
0.001132
0.001409
0.000982
0.00091
0.00074
0.000879
0.000751
0.001002
0.000666
0.000699
0.000502
0.000692
0.00089
0.001212
0.00147
0.001815
0.001354
0.001053
0.000961
0.000357
0.00301524
0.00275503
0.00232723
0.00216567
0.00175765
0.00204825
0.00228565
0.00235495
0.00263429
0.00259196
0.00302346
0.00289552
0.00273249
0.00260744
0.00258608
0.00321021
0.00288233
0.00243827
0.00215296
0.00273559
0.00246145
0.00295313
0.00307345
0.00264368
0.00315901
0.00319416
0.00340035
0.00307746
0.00319923
0.0027237
0.00315521
0.00299612
0.00325587
0.00280411
0.00241422
0.00195007
0.00162713
0.00129156
0.00156159
0.00174996
0.00175044
0.002488
2857
2873
2888
2900
2901
2911
2923
2926
2931
2948
2965
2974
2979
3000
3058
3063
3097
3115
3135
3205
3234
3287
3287
3294
3333
3386
3391
3398
3414
3419
3432
3444
3449
3496
3520
3527
3544
3557
3563
3564
3589
3614
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
0.60199005
0.606965174
0.611940299
0.616915423
0.621890547
0.626865672
0.631840796
0.63681592
0.641791045
0.646766169
0.651741294
0.656716418
0.661691542
0.666666667
0.671641791
0.676616915
0.68159204
0.686567164
0.691542289
0.696517413
0.701492537
0.706467662
0.711442786
0.71641791
0.721393035
0.726368159
0.731343284
0.736318408
0.741293532
0.746268657
0.751243781
0.756218905
0.76119403
0.766169154
0.771144279
0.776119403
0.781094527
0.786069652
0.791044776
0.7960199
0.800995025
0.805970149
7.9575274
7.9631121
7.9683195
7.972466
7.9728108
7.9762519
7.9803658
7.9813916
7.9830989
7.9888823
7.9946323
7.9976631
7.999343
8.0063676
8.0255164
8.0271501
8.0381892
8.0439844
8.0503845
8.0724674
8.081475
8.0977306
8.0977306
8.0998579
8.1116281
8.1274046
8.1288801
8.1309423
8.1356399
8.1371034
8.1408985
8.1443889
8.1458396
8.1593747
8.1662163
8.1682029
8.1730113
8.1766728
8.1783582
8.1786388
8.1856289
8.1925705
0.58801182
0.59364078
0.59890045
0.60309536
0.6034444
0.60693025
0.61110196
0.61214291
0.61387603
0.61975148
0.62559942
0.62868383
0.63039384
0.6375474
0.65705024
0.65871297
0.66993652
0.67581785
0.68230153
0.70454743
0.7135489
0.72965518
0.72965518
0.73174809
0.74325737
0.75847594
0.75988593
0.76185235
0.76631371
0.76769832
0.77127686
0.77455248
0.77590944
0.788436
0.79467114
0.79646895
0.8007958
0.80406687
0.80556555
0.80581464
0.81197877
0.81802062
25
0.65431027
0.65848916
0.66236838
0.66544501
0.66570032
0.66824442
0.67127567
0.6720298
0.67328341
0.67751514
0.68169986
0.68389635
0.68511097
0.69016841
0.70377108
0.70491883
0.71261997
0.71662446
0.72101552
0.73590749
0.74186352
0.75243301
0.75243301
0.75379891
0.76128262
0.77111529
0.77202318
0.77328857
0.77615628
0.77704545
0.77934184
0.78144185
0.78231131
0.79032638
0.7943108
0.79545933
0.79822331
0.80031294
0.80127042
0.80142957
0.8053691
0.80923386
0.000195
0.000178
0.00017
0.000191
0.00034
0.000397
0.00043
0.000609
0.000779
0.00073
0.000683
0.000786
0.00098
0.000848
0.000213
0.000321
0.000136
0.000116
8.54E-05
6.45E-05
0.000145
0.000538
0.000332
0.000235
0.000478
0.001031
0.000815
0.000652
0.000626
0.000459
0.000401
0.000336
0.000217
0.000496
0.000554
0.000414
0.000388
0.000324
0.000211
9.59E-05
0.000121
0.000145
0.0027374
0.00265472
0.00254299
0.00235512
0.0019193
0.0017122
0.00155511
0.00124002
0.00099177
0.0009455
0.00089752
0.00073875
0.00054847
0.00055233
0.00103229
0.000801
0.00096273
0.00090344
0.00086867
0.00155158
0.00162982
0.00211281
0.0016802
0.00139734
0.00159118
0.00200231
0.00165485
0.00136679
0.00121541
0.00094721
0.0007895
0.0006362
0.00044594
0.00058357
0.00053669
0.00037403
0.0002934
0.00020287
0.00010456
2.9265E-05
1.9133E-05
1.0652E-05
3618
3646
3648
3675
3709
3720
3762
3775
3812
3875
3899
3910
3910
3928
3930
3946
3976
4005
4054
4141
4208
4371
4389
4410
4442
4495
4590
4674
4703
4735
4750
4760
4765
4784
4967
5083
5547
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
0.810945274
0.815920398
0.820895522
0.825870647
0.830845771
0.835820896
0.84079602
0.845771144
0.850746269
0.855721393
0.860696517
0.865671642
0.870646766
0.875621891
0.880597015
0.885572139
0.890547264
0.895522388
0.900497512
0.905472637
0.910447761
0.915422886
0.92039801
0.925373134
0.930348259
0.935323383
0.940298507
0.945273632
0.950248756
0.955223881
0.960199005
0.965174129
0.970149254
0.975124378
0.980099502
0.985074627
0.990049751
8.1936767
8.201386
8.2019344
8.2093084
8.2185176
8.2214789
8.232706
8.2361557
8.2459093
8.2623009
8.2684754
8.2712927
8.2712927
8.2758857
8.2763947
8.2804577
8.2880316
8.2952989
8.3074593
8.3286926
8.3447428
8.3827471
8.3868567
8.39163
8.39886
8.4107209
8.4316353
8.4497705
8.4559559
8.462737
8.4658999
8.4680029
8.4690528
8.4730323
8.5105713
8.5336569
8.6210125
0.81897593
0.82557481
0.82604023
0.83224608
0.83985543
0.84226819
0.85125983
0.85397212
0.86150891
0.8737226
0.87817184
0.88017383
0.88017383
0.88339958
0.88375415
0.88656325
0.89169913
0.89650267
0.90426432
0.91697554
0.92586591
0.94444924
0.94625296
0.94829833
0.95129558
0.9559527
0.9633976
0.96909165
0.97087859
0.97274991
0.97359194
0.97414112
0.97441211
0.97542027
0.98353356
0.98738722
0.99607032
0.80984536
0.81407349
0.81437202
0.81835728
0.8232585
0.82481664
0.83064438
0.83240974
0.83733677
0.84540254
0.84837104
0.84971283
0.84971283
0.85188334
0.8521226
0.854023
0.8575216
0.86082485
0.86623483
0.87533077
0.88191312
0.89650906
0.89800527
0.89972328
0.90228515
0.90638346
0.91329842
0.9189792
0.92085107
0.9228654
0.92379151
0.9244026
0.92470626
0.92584883
0.93598428
0.94166069
0.95964275
6.45E-05
9.32E-05
2.65E-05
4.06E-05
8.12E-05
4.16E-05
0.000109
6.73E-05
0.000116
0.000324
0.000305
0.00021
9.08E-05
6.05E-05
9.97E-06
9.82E-07
1.33E-06
9.61E-07
1.42E-05
0.000132
0.000238
0.000843
0.000668
0.000526
0.000439
0.000426
0.000534
0.000567
0.000426
0.000307
0.000179
8.04E-05
1.82E-05
8.76E-08
1.18E-05
5.35E-06
3.62E-05
1.2098E-06
3.4111E-06
4.2556E-05
5.6451E-05
5.7567E-05
0.00012109
0.00010306
0.00017853
0.00017981
0.00010648
0.00015192
0.00025468
0.00043823
0.00056352
0.00081079
0.00099535
0.00109069
0.00120392
0.00117393
0.00090853
0.00081423
0.00035773
0.00050143
0.00065792
0.00078754
0.00083752
0.000729
0.0006914
0.00086422
0.00104707
0.00132551
0.00166232
0.00206507
0.00242808
0.00194615
0.00188477
0.00092459
5614
200
0.995024876
8.6330188
0.99672322
0.96171772
2.88E-06
0.00110937
MEAN
Std. Dev.
2611.3
1104.4
Log Normal Dist.
7.7623597
0.4916265
MSE
AIC
26
SUM
0.110786
0.31773261
Normal Dist.
Log Normal Dist.
0.000554
0.00158866
-647.309
-555.79364
CUMULATIVE
522267
1552.4719
BIC
-646.707
-557.49261
1,2
1
0,8
Normal Cdf
0,6
Log. Norm Cdf
0,4
0,2
0
0
1000
2000
3000
4000
5000
27
6000
Analysis of rainfall data of Year 1950 - 2000 is below
Increasing
Order
Rainfall
355
695
820
834
835
860
939
952
1008
1013
1020
1027
1036
1055
1057
1063
1066
1108
1110
1116
1170
1182
1225
1248
1260
1264
1277
1366
1408
1420
1421
1431
1432
1447
1458
1494
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Weibull
Distribution
0.0049751
0.0099502
0.0149254
0.0199005
0.0248756
0.0298507
0.0348259
0.039801
0.0447761
0.0497512
0.0547264
0.0597015
0.0646766
0.0696517
0.0746269
0.079602
0.0845771
0.0895522
0.0945274
0.0995025
0.1044776
0.1094527
0.1144279
0.119403
0.1243781
0.1293532
0.1343284
0.1393035
0.1442786
0.1492537
0.1542289
0.159204
0.1641791
0.1691542
0.1741294
0.1791045
ln Rainfall
5.8721178
6.5439118
6.7093043
6.7262334
6.7274317
6.7569324
6.8448155
6.858565
6.9157234
6.9206715
6.9275579
6.9343972
6.9431224
6.961296
6.96319
6.9688504
6.9716686
7.0103119
7.0121153
7.0175061
7.064759
7.0749632
7.1106961
7.1292975
7.138867
7.1420366
7.1522689
7.219642
7.2499255
7.2584122
7.2591161
7.2661288
7.2668273
7.2772477
7.2848209
7.3092124
Normal
Cdf
0.0265744
0.0505553
0.0628445
0.0643547
0.0644637
0.0672341
0.0765956
0.0782268
0.0855558
0.0862344
0.0871911
0.0881558
0.0894077
0.0920941
0.0923803
0.0932429
0.0936764
0.0999027
0.1002065
0.1011221
0.1096381
0.1115985
0.1188289
0.1228294
0.1249537
0.1256675
0.1280069
0.1448346
0.1532714
0.1557405
0.1559475
0.1580269
0.1582358
0.1613915
0.1637317
0.1715434
28
Log. Norm
Cdf
4.53E-05
0.0059227
0.0149052
0.0162836
0.0163852
0.0190626
0.0293351
0.0312981
0.040656
0.041563
0.0428526
0.0441652
0.0458866
0.049645
0.0500504
0.0512778
0.0518978
0.0610133
0.0614675
0.0628409
0.0759232
0.0790031
0.0905358
0.0970131
0.1004749
0.1016412
0.1054734
0.1333296
0.1473698
0.151476
0.15182
0.1552751
0.1556221
0.1608589
0.1647362
0.1776317
(C-E)2
0.0004665
0.0016488
0.0022962
0.0019762
0.0015672
0.0013975
0.0017447
0.0014765
0.001663
0.001331
0.001054
0.0008096
0.0006116
0.0005037
0.0003152
0.0001861
8.28E-05
0.0001071
3.225E-05
2.623E-06
2.663E-05
4.604E-06
1.937E-05
1.174E-05
3.313E-07
1.358E-05
3.996E-05
3.059E-05
8.087E-05
4.208E-05
2.954E-06
1.386E-06
3.532E-05
6.026E-05
0.0001081
5.717E-05
(C-F)2
2.43E-05
1.622E-05
4.085E-10
1.308E-05
7.209E-05
0.0001164
3.015E-05
7.23E-05
1.698E-05
6.705E-05
0.000141
0.0002414
0.0003531
0.0004003
0.000604
0.0008023
0.0010679
0.0008145
0.001093
0.0013441
0.0008154
0.0009272
0.0005708
0.0005013
0.0005714
0.000768
0.0008326
3.569E-05
9.555E-06
4.938E-06
5.803E-06
1.544E-05
7.322E-05
6.881E-05
8.823E-05
2.169E-06
1506
1526
1531
1546
1549
1567
1578
1583
1617
1618
1639
1656
1662
1685
1714
1720
1724
1728
1737
1746
1870
1878
1881
1892
1895
1908
1913
1967
1972
1994
2022
2045
2069
2070
2074
2078
2083
2103
2122
2133
2141
2149
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
0.1840796
0.1890547
0.1940299
0.199005
0.2039801
0.2089552
0.2139303
0.2189055
0.2238806
0.2288557
0.2338308
0.238806
0.2437811
0.2487562
0.2537313
0.2587065
0.2636816
0.2686567
0.2736318
0.278607
0.2835821
0.2885572
0.2935323
0.2985075
0.3034826
0.3084577
0.3134328
0.318408
0.3233831
0.3283582
0.3333333
0.3383085
0.3432836
0.3482587
0.3532338
0.358209
0.3631841
0.3681592
0.3731343
0.3781095
0.3830846
0.3880597
7.3172124
7.3304052
7.3336764
7.3434262
7.3453648
7.3569182
7.3639135
7.3670771
7.3883279
7.3889461
7.4018416
7.4121603
7.415777
7.4295208
7.4465851
7.4500796
7.4524025
7.4547199
7.4599148
7.4650827
7.5336937
7.5379627
7.5395588
7.5453897
7.5469741
7.5538109
7.556428
7.5842648
7.5868035
7.597898
7.6118424
7.6231531
7.6348207
7.6353039
7.6372344
7.6391612
7.6415644
7.6511202
7.6601143
7.6652847
7.6690283
7.6727579
0.1741994
0.1786838
0.1798161
0.1832402
0.1839298
0.1881016
0.1906796
0.1918585
0.199993
0.2002353
0.2053652
0.2095747
0.2110724
0.2168714
0.2243129
0.2258704
0.2269121
0.2279566
0.2303164
0.2326899
0.2667361
0.269016
0.2698735
0.2730293
0.2738931
0.2776519
0.2791042
0.2950207
0.2965153
0.3031327
0.3116488
0.3187207
0.326171
0.326483
0.3277321
0.3289831
0.3305496
0.3368449
0.3428682
0.3463739
0.3489317
0.3514965
29
0.1819964
0.1893391
0.1911876
0.1967624
0.1978825
0.2046373
0.2087929
0.2106885
0.2236811
0.2240658
0.2321749
0.2387796
0.2411185
0.2501196
0.2615385
0.2639095
0.2654916
0.2670748
0.270641
0.2742121
0.3237023
0.3269003
0.3280993
0.3324944
0.3336926
0.3388826
0.3408775
0.3623621
0.3643445
0.3730497
0.3840833
0.3931029
0.4024676
0.4028567
0.4044121
0.4059661
0.4079064
0.4156431
0.4229553
0.4271709
0.4302285
0.4332788
9.762E-05
0.0001076
0.000202
0.0002485
0.000402
0.0004349
0.0005406
0.0007315
0.0005706
0.0008191
0.0008103
0.0008545
0.0010699
0.0010166
0.0008654
0.0010782
0.001352
0.0016565
0.0018762
0.0021084
0.0002838
0.0003819
0.0005597
0.0006491
0.0008755
0.000949
0.0011785
0.000547
0.0007219
0.0006363
0.0004702
0.0003837
0.0002928
0.0004742
0.0006503
0.0008542
0.001065
0.0009806
0.000916
0.0010071
0.0011664
0.0013369
4.34E-06
8.089E-08
8.078E-06
5.029E-06
3.718E-05
1.864E-05
2.639E-05
6.752E-05
3.979E-08
2.294E-05
2.742E-06
6.979E-10
7.089E-06
1.859E-06
6.095E-05
2.707E-05
3.276E-06
2.502E-06
8.945E-06
1.931E-05
0.0016096
0.0014702
0.0011949
0.0011551
0.0009126
0.0009257
0.0007532
0.001932
0.0016778
0.0019973
0.0025756
0.0030024
0.0035028
0.0029809
0.0026192
0.0022807
0.0020001
0.0022547
0.0024821
0.002407
0.0022225
0.0020448
2184
2193
2196
2210
2214
2214
2234
2243
2254
2288
2288
2292
2296
2321
2331
2346
2359
2379
2383
2384
2411
2419
2420
2445
2490
2509
2563
2564
2620
2628
2641
2653
2655
2656
2668
2671
2683
2702
2708
2729
2746
2793
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
0.3930348
0.39801
0.4029851
0.4079602
0.4129353
0.4179104
0.4228856
0.4278607
0.4328358
0.4378109
0.4427861
0.4477612
0.4527363
0.4577114
0.4626866
0.4676617
0.4726368
0.4776119
0.4825871
0.4875622
0.4925373
0.4975124
0.5024876
0.5074627
0.5124378
0.5174129
0.5223881
0.5273632
0.5323383
0.5373134
0.5422886
0.5472637
0.5522388
0.5572139
0.5621891
0.5671642
0.5721393
0.5771144
0.5820896
0.5870647
0.5920398
0.5970149
7.6889133
7.6930257
7.6943928
7.7007478
7.7025561
7.7025561
7.711549
7.7155695
7.7204617
7.7354334
7.7354334
7.7371801
7.7389238
7.7497534
7.7540526
7.760467
7.7659931
7.7744355
7.7761155
7.776535
7.7877969
7.7911095
7.7915228
7.8018004
7.820038
7.8276395
7.8489337
7.8493238
7.8709296
7.8739784
7.8789129
7.8834464
7.8841999
7.8845765
7.8890844
7.8902082
7.8946909
7.9017475
7.9039656
7.9116905
7.9179006
7.9348716
0.3627955
0.3657209
0.3666977
0.3712678
0.3725769
0.3725769
0.3791442
0.382111
0.3857466
0.397046
0.397046
0.3983812
0.3997177
0.4080965
0.41146
0.4165175
0.4209119
0.4276915
0.4290501
0.4293899
0.4385828
0.4413132
0.4416547
0.4502057
0.4656532
0.4721925
0.4908127
0.4911579
0.5104884
0.5132489
0.5177334
0.5218709
0.5225603
0.522905
0.5270395
0.5280727
0.5322035
0.5387367
0.5407978
0.5480024
0.5538233
0.5698522
30
0.4465354
0.4499201
0.4510461
0.4562853
0.4577776
0.4577776
0.4652072
0.4685329
0.4725825
0.4849915
0.4849915
0.4864404
0.487887
0.4968743
0.5004428
0.5057668
0.5103527
0.5173559
0.518749
0.5190968
0.5284278
0.5311698
0.5315118
0.5400081
0.5550377
0.56128
0.578681
0.5789984
0.5964949
0.5989493
0.6029133
0.6065458
0.6071488
0.60745
0.6110505
0.6119466
0.6155151
0.6211129
0.6228673
0.6289571
0.6338295
0.6470333
0.0009144
0.0010426
0.0013168
0.0013463
0.0016288
0.0020551
0.0019133
0.002093
0.0022174
0.0016618
0.0020922
0.0024384
0.002811
0.0024616
0.0026242
0.0026157
0.0026755
0.002492
0.0028662
0.003384
0.0029111
0.0031584
0.0037006
0.0032784
0.0021888
0.0020449
0.000997
0.0013108
0.0004774
0.0005791
0.000603
0.0006448
0.0008808
0.0011771
0.0012355
0.0015281
0.0015949
0.0014728
0.001705
0.0015259
0.0014605
0.0007378
0.0028623
0.0026947
0.0023099
0.0023353
0.0020108
0.0015894
0.0017911
0.0016542
0.0015798
0.002226
0.0017813
0.0014961
0.0012356
0.0015337
0.0014255
0.001452
0.0014225
0.0015796
0.0013077
0.0009944
0.0012881
0.0011328
0.0008424
0.0010592
0.0018147
0.0019243
0.0031689
0.0026662
0.0041161
0.003799
0.0036754
0.0035144
0.0030151
0.0025237
0.0023874
0.0020055
0.0018815
0.0019359
0.0016628
0.001755
0.0017464
0.0025018
2809
2811
2860
2868
2869
2875
2879
2888
2897
2915
2950
2955
3024
3035
3072
3073
3074
3076
3103
3111
3132
3135
3173
3174
3181
3187
3208
3208
3225
3234
3243
3264
3279
3298
3324
3406
3410
3420
3422
3472
3529
3551
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
0.60199
0.6069652
0.6119403
0.6169154
0.6218905
0.6268657
0.6318408
0.6368159
0.641791
0.6467662
0.6517413
0.6567164
0.6616915
0.6666667
0.6716418
0.6766169
0.681592
0.6865672
0.6915423
0.6965174
0.7014925
0.7064677
0.7114428
0.7164179
0.721393
0.7263682
0.7313433
0.7363184
0.7412935
0.7462687
0.7512438
0.7562189
0.761194
0.7661692
0.7711443
0.7761194
0.7810945
0.7860697
0.7910448
0.7960199
0.800995
0.8059701
7.9405838
7.9412956
7.9585769
7.9613702
7.9617188
7.963808
7.9651983
7.9683195
7.971431
7.9776251
7.9895604
7.9912539
8.0143357
8.0179667
8.0300841
8.0304096
8.0307349
8.0313853
8.0401247
8.0426995
8.0494271
8.0503845
8.0624328
8.0627479
8.0649509
8.0668353
8.073403
8.073403
8.0786882
8.081475
8.0842541
8.0907087
8.0952938
8.1010715
8.1089242
8.1332939
8.1344676
8.1373958
8.1379805
8.1524861
8.1687698
8.1749845
0.5752841
0.5759621
0.5924982
0.5951832
0.5955185
0.5975289
0.5988678
0.6018759
0.604878
0.6108633
0.6224254
0.6240684
0.6465015
0.6500336
0.6618176
0.662134
0.6624502
0.6630824
0.6715707
0.6740691
0.6805901
0.6815172
0.6931604
0.6934642
0.6955875
0.6974022
0.7037151
0.7037151
0.7087808
0.7114462
0.7141001
0.7202468
0.7245978
0.7300607
0.7374474
0.760047
0.7611216
0.7637966
0.7643296
0.7774372
0.7918597
0.7972754
31
0.6514389
0.6519864
0.6651809
0.6672951
0.6675586
0.6691359
0.6701839
0.6725318
0.6748657
0.6794912
0.6883254
0.6895703
0.706317
0.7089128
0.7174974
0.7177263
0.717955
0.718412
0.7245171
0.7263033
0.7309432
0.7316003
0.7397997
0.7400124
0.7414969
0.7427633
0.7471515
0.7471515
0.750654
0.7524904
0.7543144
0.7585229
0.7614885
0.7651969
0.7701856
0.7852834
0.7859957
0.7877668
0.7881194
0.7967571
0.8061988
0.8097306
0.0007132
0.0009612
0.000378
0.0004723
0.0006955
0.0008606
0.0010872
0.0012208
0.0013626
0.001289
0.0008594
0.0010659
0.0002307
0.0002767
9.651E-05
0.0002098
0.0003664
0.0005515
0.0003989
0.0005039
0.0004369
0.0006225
0.0003342
0.0005269
0.0006659
0.000839
0.0007633
0.001063
0.0010571
0.0012126
0.0013797
0.001294
0.0013393
0.0013038
0.0011355
0.0002583
0.0003989
0.0004961
0.0007137
0.0003453
8.345E-05
7.56E-05
0.0024452
0.0020269
0.0028346
0.0025381
0.0020856
0.0017868
0.0014702
0.0012756
0.0010939
0.0010709
0.0013384
0.0010794
0.0019914
0.0017847
0.0021027
0.00169
0.0013223
0.0010141
0.0010873
0.0008872
0.0008673
0.0006316
0.0008041
0.0005567
0.0004042
0.0002688
0.0002499
0.0001174
8.762E-05
3.871E-05
9.429E-06
5.308E-06
8.671E-08
9.452E-07
9.19E-07
8.398E-05
2.402E-05
2.88E-06
8.558E-06
5.434E-07
2.708E-05
1.414E-05
3559
3624
3634
3642
3656
3693
3713
3745
3772
3779
3821
3823
3856
3899
3940
4019
4095
4105
4153
4170
4207
4219
4251
4253
4395
4423
4636
4728
4749
4877
4948
5035
5061
5124
5308
5570
5949
7527
MEAN
Std. Dev.
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
2589.615
1155.61
0.8109453
0.8159204
0.8208955
0.8258706
0.8308458
0.8358209
0.840796
0.8457711
0.8507463
0.8557214
0.8606965
0.8656716
0.8706468
0.8756219
0.880597
0.8855721
0.8905473
0.8955224
0.9004975
0.9054726
0.9104478
0.9154229
0.920398
0.9253731
0.9303483
0.9353234
0.9402985
0.9452736
0.9502488
0.9552239
0.960199
0.9651741
0.9701493
0.9751244
0.9800995
0.9850746
0.9900498
0.9950249
8.1772349
8.1953337
8.1980892
8.2002883
8.2041249
8.2141944
8.2195955
8.2281769
8.2353606
8.2372147
8.2482674
8.2487907
8.2573857
8.2684754
8.278936
8.2987884
8.317522
8.319961
8.3315862
8.3356713
8.3445051
8.3473534
8.3549095
8.3553799
8.3882228
8.3945735
8.4416072
8.4612576
8.4656893
8.4922856
8.5067387
8.5241688
8.5293194
8.5416907
8.5769704
8.6251503
8.6909784
8.9262518
0.7992236
0.8146328
0.8169366
0.8187666
0.8219416
0.8301625
0.8345032
0.8412976
0.8468862
0.8483135
0.8566913
0.8570823
0.8634296
0.8714072
0.878707
0.8919397
0.9036572
0.9051267
0.9119507
0.9142777
0.9191826
0.920727
0.924736
0.9249814
0.9408888
0.943688
0.9617052
0.9678748
0.9691615
0.9761131
0.9793653
0.9828318
0.9837659
0.9858504
0.9906721
0.9950465
0.9981756
0.9999903
Log Normal Dist.
7.7535192
0.4806288
MSE
AIC
32
0.8109997 0.0001374 2.959E-09
0.8210157 1.658E-06 2.596E-05
0.8225108 1.567E-05 2.609E-06
0.8236982 5.047E-05 4.719E-06
0.825758 7.928E-05 2.589E-05
0.8310907 3.202E-05 2.237E-05
0.8339074 3.96E-05 4.745E-05
0.8383199 2.001E-05 5.552E-05
0.8419545 1.49E-05
7.73E-05
0.8428837 5.488E-05 0.0001648
0.8483487 1.604E-05 0.0001525
0.8486043 7.378E-05 0.0002913
0.852761 5.209E-05 0.0003199
0.8580101 1.776E-05 0.0003102
0.862844 3.572E-06 0.0003152
0.8717057 4.055E-05 0.0001923
0.879696 0.0001719 0.0001177
0.8807099 9.224E-05 0.0002194
0.8854597 0.0001312 0.0002261
0.8870964 7.753E-05 0.0003377
0.8905784 7.63E-05 0.0003948
0.8916845 2.813E-05 0.0005635
0.8945797 1.882E-05 0.0006666
0.8947581 1.535E-07 0.0009373
0.9066775 0.0001111 0.0005603
0.9088624 6.997E-05 0.0007002
0.9238767 0.0004582 0.0002697
0.9295605 0.0005108 0.0002469
0.9307961 0.0003577 0.0003784
0.9378635 0.0004364 0.0003014
0.9414607 0.0003673 0.0003511
0.945579 0.0003118 0.000384
0.946751 0.0001854 0.0005475
0.9494845 0.000115 0.0006574
0.9566694 0.0001118 0.000549
0.9651244 9.944E-05 0.000398
0.9744408 6.603E-05 0.0002436
0.9926563 2.466E-05 5.61E-06
SUM
0.1653102 0.190798
Normal Dist.
Log Normal Dist.
0.0008266
0.000954
-612.54607
-600.09124
CUMULATIVE
517923
1550.7038
BIC
-611.94401
-601.79021
1,2
1
0,8
Normal Cdf
0,6
Log. Normal Cdf
0,4
0,2
0
0
1000
2000
3000
4000
5000
6000
33
7000
8000
Analysis of rainfall data of Year 2000 - 2016 is below
Increasing
Order
Rainfall
741
910
917
941
992
1002
1023
1286
1315
1322
1332
1367
1511
1515
1542
1559
1566
1613
1624
1628
1680
1698
1733
1759
1819
1953
2019
2084
2087
2130
2171
2180
2211
2218
2246
2339
Rank
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Weibull
Distribution
0.0153846
0.0307692
0.0461538
0.0615385
0.0769231
0.0923077
0.1076923
0.1230769
0.1384615
0.1538462
0.1692308
0.1846154
0.2
0.2153846
0.2307692
0.2461538
0.2615385
0.2769231
0.2923077
0.3076923
0.3230769
0.3384615
0.3538462
0.3692308
0.3846154
0.4
0.4153846
0.4307692
0.4461538
0.4615385
0.4769231
0.4923077
0.5076923
0.5230769
0.5384615
0.5538462
ln Rainfall
6.6080006
6.8134446
6.8211075
6.8469431
6.8997231
6.9097533
6.9304948
7.1592919
7.1815919
7.186901
7.1944369
7.2203738
7.320527
7.3231707
7.3408356
7.3517999
7.3562799
7.3858511
7.3926475
7.3951075
7.4265491
7.4372064
7.4576093
7.4725007
7.5060422
7.5771219
7.6103576
7.6420444
7.6434829
7.6638773
7.6829432
7.6870802
7.7012002
7.7043612
7.7169061
7.7574788
Normal Cdf
0.04512531
0.06544122
0.06641529
0.06984032
0.07756802
0.07915665
0.08257278
0.13512414
0.142082
0.14379719
0.1462716
0.15515611
0.19537498
0.19657571
0.20479702
0.21007671
0.21227374
0.22736907
0.2309874
0.23231109
0.24989757
0.25614585
0.26852447
0.27791077
0.30016345
0.35253842
0.37948463
0.4066083
0.40787215
0.42608656
0.4436025
0.4474635
0.46079837
0.46381613
0.47590626
0.51616023
34
Log. Normal
Cdf
0.008112031
0.026684396
0.027789454
0.031799711
0.041482072
0.043568176
0.048150509
0.127663998
0.138677716
0.141392468
0.145307328
0.159334652
0.221498712
0.22330803
0.235611062
0.243431576
0.246666934
0.268587683
0.273760708
0.275645197
0.300276481
0.308845534
0.325541116
0.337954137
0.366548985
0.429465493
0.459619733
0.4885893
0.48990704
0.508594322
0.526048115
0.529829861
0.542715108
0.545594015
0.556994438
0.593497002
(C-E)2
0.000885
0.001202
0.000411
6.89E-05
4.16E-07
0.000173
0.000631
0.000145
1.31E-05
0.000101
0.000527
0.000868
2.14E-05
0.000354
0.000675
0.001302
0.002427
0.002456
0.00376
0.005682
0.005355
0.006776
0.00728
0.008339
0.007132
0.002253
0.001289
0.000584
0.001465
0.001257
0.00111
0.002011
0.002199
0.003512
0.003913
0.00142
(C-F)2
5.28905E-05
1.66859E-05
0.000337251
0.000884393
0.001256065
0.00237554
0.003545226
2.10413E-05
4.67326E-08
0.000155094
0.000572331
0.000639115
0.000462195
6.27805E-05
2.34433E-05
7.41075E-06
0.000221162
6.94788E-05
0.000343991
0.001027017
0.00051986
0.000877108
0.000801175
0.000978228
0.000326395
0.000868215
0.001956746
0.00334316
0.001914342
0.002214254
0.002413269
0.001407913
0.001226597
0.000507019
0.000343468
0.00157219
2345
2527
2666
2744
2761
2782
2829
2942
2977
2995
3008
3040
3063
3075
3083
3156
3158
3243
3252
3315
3333
3417
3436
3602
3695
3876
3976
4978
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
0.5692308
0.5846154
0.6
0.6153846
0.6307692
0.6461538
0.6615385
0.6769231
0.6923077
0.7076923
0.7230769
0.7384615
0.7538462
0.7692308
0.7846154
0.8
0.8153846
0.8307692
0.8461538
0.8615385
0.8769231
0.8923077
0.9076923
0.9230769
0.9384615
0.9538462
0.9692308
0.9846154
7.7600407
7.8347881
7.8883345
7.917172
7.9233482
7.9309254
7.9476786
7.9868449
7.9986714
8.0046995
8.0090307
8.0196128
8.0271501
8.0310602
8.0336584
8.0570607
8.0576942
8.0842541
8.0870255
8.1062129
8.1116281
8.1365183
8.1420633
8.1892445
8.2147358
8.262559
8.2880316
8.5127835
0.518756
0.59661261
0.65375216
0.68443533
0.69096624
0.69895109
0.71647573
0.75649203
0.76823743
0.7741528
0.77837137
0.78856145
0.79571303
0.79938641
0.80181314
0.82312898
0.82369181
0.84656034
0.84886118
0.8643223
0.8685334
0.88698818
0.89089271
0.92094831
0.93478759
0.95626531
0.96542576
0.99816431
0.595778321
0.660611192
0.704410891
0.72686871
0.731566289
0.737273376
0.749667734
0.777390765
0.785404413
0.789423732
0.792284109
0.79917543
0.803999178
0.806473626
0.808107313
0.822438619
0.822816943
0.838218534
0.839773768
0.85027245
0.853150468
0.865899488
0.868632893
0.890338205
0.900932469
0.918753243
0.927199348
0.975667065
SUM
Log Normal Dist.
0.002548
0.000144
0.002889
0.004768
0.003624
0.002788
0.003018
0.006331
0.005765
0.004417
0.003057
0.00251
0.001753
0.000909
0.000296
0.000535
6.9E-05
0.000249
7.33E-06
7.75E-06
7.04E-05
2.83E-05
0.000282
4.53E-06
1.35E-05
5.85E-06
1.45E-05
0.000184
0.123885
0.000704772
0.005775363
0.010901634
0.012428703
0.010160047
0.008302769
0.007766769
0.010093756
0.008666999
0.006680026
0.004789635
0.003686177
0.002515326
0.00138703
0.000551871
0.000503492
5.52395E-05
5.54921E-05
4.07054E-05
0.000126923
0.000565137
0.000697393
0.001525638
0.001071824
0.001408431
0.001231512
0.00176664
8.00724E-05
0.123884916
Normal Dist.
Log Normal Dist.
MEAN
2589.615
7.7535192
MSE
0.0008266
0.000954
Std. Dev.
1155.61
0.4806288
AIC
-612.54607
-600.09124
CUMULATIVE
517923
1550.7038
BIC
-611.94401
-601.79021
35
1,2
1
0,8
Normal Cdf
0,6
Log. Normal Cdf
0,4
0,2
0
0
1000
2000
3000
4000
36
5000
6000
Based on the norm plot and lognorm plot for all the data set we can conclude that all the data set
is more accurately fitting in normal distribution.
Chi square test for 1871-1900
Chi square test for normal distribution
∑(Oi-Ei)^2/(Ei)= 0.098391
From the table of critical values of chi square distribution (n =120, Distribution parameter =2,
Significance level = 0.05) is 144.3537
So ,
∑(Oi-Ei)^2/(Ei) < X2 (.05,118)
So following data is following normal distribution
Log Normal distribution (1871-1900)
∑(Oi-Ei)^2/(Ei)= 0.35671
From the table of critical values of chi square distribution (n =120, Distribution parameter =2,
Significance level = 0.05) is 144.353
So following data set is also following log normal distribution .
Chi square test for(1901-1951)
Normal distribution (1901-1950)
∑(Oi-Ei)^2/(Ei)= 0.066098
From the table of critical values of chi square distribution (n =200, Distribution parameter =2,
Significance level = 0.05) is 231.8292
So ,
∑(Oi-Ei)^2/(Ei) < X2 (.05,198)
So following data is following normal distribution
Log Normal distribution (1901-1950)
37
∑(Oi-Ei)^2/(Ei)= 0.755482
From the table of critical values of chi square distribution (n =200, Distribution parameter =2,
Significance level = 0.05) is 231.8292
So following data set is also following log normal distribution .
Chi test for (1951-2000)
Normal distribution (1951-2000)
∑(Oi-Ei)^2/(Ei)= 0.09371462
From the table of critical values of chi square distribution (n =200, Distribution parameter =2,
Significance level = 0.05) is 231.8292
So ,
∑(Oi-Ei)^2/(Ei) < X2 (.05,198)
So following normal distribution for this set
Log Normal distribution (1951-2000)
∑(Oi-Ei)^2/(Ei)= 0.236163573
From the table of critical values of chi square distribution (n =200, Distribution parameter =2,
Significance level = 0.05) is 231.8292
So following data set is also following log normal distribution .
38
Chi test for (2000-2016)
Normal distribution (2000-2016)
∑(Oi-Ei)^2/(Ei)=
From the table of critical values of chi square distribution (n = 64 , Distribution parameter =2 ,
Significance level = 0.05) is 81.381
So ,
∑(Oi-Ei)^2/(Ei) < X2 ( 0.05, 62 )
So following normal distribution for this set
Log Normal distribution (2000-2016)
∑(Oi-Ei)^2/(Ei)=
From the table of critical values of chi square distribution (n = 64 , Distribution parameter = 2,
Significance level = 0.05) is 81.381
So following data set is also following log normal distribution .
Since all the data set is following both lognormal and normal distribution
So, Checking the best distribution on the basis of Aic and Bic value.
For rainfall data from 1871-1900)
Ai c value for normal distribution is = -405.9252
Bic value for normal distribution is = -406.0835
Aic value for lognormal distribution is = - 341.0252893
Bic value for lognormal distribution is = -342.9461081
39
For rainfall data from 1901-1950
Aic Bic value for normal distribution is = -663.1393
Bic value for normal distribution is = - 663.7413
Aic value for lognormal distribution is =-547.15
Bic value for lognormal distribution is = - 546.548499
For rainfall data from 1951-2000
Aic value Bic value for normal distribution is = -616.1305596
Bic value for normal distribution is = -616.7326196
Aic value for lognormal distribution is = -603.0344216
Bic value for lognormal distribution is = -602.4323616
For rainfall data from 2000-2016
Aic value for normal distribution is =
Bic value for normal distribution is =
Aic value for lognormal distribution is =
Bic value for lognormal distribution is =
40
SUMMARY:• The rainfall data in the period from 1871-1900 follows normal distribution.
• The rainfall data in the period from 1901-1950 follows normal distribution.
• The rainfall data in the period from 1951-2000 follows normal distribution.
• The rainfall data in the period from 2000-2016 follows normal distribution.
The final plot of Cdf’s for the 4 data sets is as shown:-
1,2
1
0,8
Normal Cdf 1871-1900
Normal Cdf 1901-1950
0,6
Normal Cdf 1951-2000
0,4
Normal Cdf 2001-2016
0,2
0
0
2000
4000
6000
8000
41
42
CHAPTER 6
FUTURE SCOPE OF THIS WORK
All the information regarding the project will be taken from tropmet pune. The
rainfall data of last 146 years have been analyzed on the basis of Weibull, Normal, Log
-Normal methods of probability distribution .The best fit method which has the
minimum difference in value according to the Chi Square Method has been used to find
out the rainfall pattern in the upcoming future. This analysis will provide useful
information for water resources planners, farmers and urban engineers to assess the
availability of water and create the storage accordingly. Frequency of probability
distribution helps to relate the magnitude of the extreme events like floods, droughts and
severe storms with number of occurrences such that their chance of occurrence with
time can be predicted easily.
43
REFERENCES
1. Suchit Kumar Rai, Sunil Kumar, Arvind Kumar Rai, Satyapriya and Dana Ram Palsaniya
2014 Climate Change Variability and Rainfall Probability for Crop Planning in Few
Districts of Central India. Atmos. Climate Sci. 4 394-403.
2. Nyatuame M, Owusu-Gyimah V and Ampiaw F 2014 Statistical Analysis of Rainfall
Trend for Volta Region in Ghana Int. J. Atmos. Sci. 67(2) 1-11.
3. Rajendran V, Venkatasubramani R and Vijayakumar G 2016 Rainfall variation and
frequency analysis study in Dharmapuri district (India). Indian J. Geo. Mar. Sci 45(11)
1560-5.
4. Engineering Hydrology by K.Subramanya
5. Applied Hydrology by V.T.chow
44
45
46