Statistical Analysis & Asthmatic Patients in Sulaimaniyah
Governorate in the tuber-closes center
Dr.Mohammad M.Faqe Hussain(1)
University of Sulaimani
School of Administration and Economics
Statistical Department
faqi_zanko@yahoo.co.uk
Asst. Lecturer Roqia Abdulkadir Jamel(2)
Presidency of Slemani Polytechnic University
Technical Institute of Slemani
Statistics and informatics department
Roqia_Abdulkadir@yahoo.com
Abstract
This paper is study the people who was affected with asthma diseases during the
period (2005-2011). Asthma is a disease affecting the airways that carry air to and from
your lungs. People who suffer from this chronic condition (long-lasting or recurrent) are
said to be asthmatic. The inside walls of an asthmatic's airways are swollen or inflamed.
This swelling or inflammation makes the airways extremely sensitive to irritations and
increases your susceptibility to an allergic reaction. in this study applied two models, the
first model is single exponential smoothing model(SESM) and second model is the
double exponential smoothing model (SDEM) ,and after that it compare between the two
models depending on the measures (MAPE, MAD, MSD), and after the process of
comparison the double exponential smoothing model was selected ". Depending on the
double exponential smoothing model the confidence limit and prediction of numbers of
people who is affected with these diseases are obtained subsequent the years 2012 and
2013. In the final of this study the number of male and female affected with asthma
disease are increasing in the years 2012 and 2013
for both genders .The study
recommend that the Ministry of Health must be more attention and care, for the patients
who affected with this type of the disease in the sulaymaniyah governorate and then
supply of medicines and open more health centers for the purpose of their care and
treatments.
Keywords: Method of Analysis, the model, Forecasting Performance Measures, Analysis
the data
1 Method of Analysis [2][4]
In this paper, two different types of univariate forecasting model were developed
on the same data set for the purpose of finding the best fit models. These models are
Single Exponential Model, Double Exponential Model. The application of univariate
models (Single Exponential Model, Double Exponential Model) as forecasting provide
the advantage of simplicity, less costly to develop and easier to understand. Each model
type has its unique characteristics which define its suitability to be fitted to that data. Data
collected were analyzed using Microsoft Office Excel and MINITAB.
2 The Model
2-1 Single Exponential Smoothing Model [1][3][6]
Single exponential smoothing model is the simplest model in the group of the
exponential smoothing techniques. The model requires only one parameter, which is
constant, α, to generate the fitted values and forecast. In this model, the forecast for the
next and all subsequent periods are determined by adjusting the current period forecast by
a portion of the difference between the current forecast and current actual value. Hence,
mathematically the model can represented as:
𝐹𝑡+𝑚 = 𝛼𝑦𝑡 + (1 − 𝛼)𝐹𝑡 ………..(1)
Where:
𝐹𝑡+𝑚 = single exponential smoothed value in period 𝑡 + 𝑚
𝑦𝑡
= the actual value at time period 𝑡
𝛼
= unknown smoothing constant to be determined.
The 𝛼 value is between 0 and 1.
𝐹𝑡
= the forecast made in period 𝑡
The best parameter value, α can be determined by using solver facility that available in
Excel software based on the estimation part of the data. The best value of α is defined
based on the smallest value of MSD
2-1 Double Exponential Smoothing Model [1][3] [6]
This model is useful for series that exhibits a linear trend characteristic, the main
advantage of double exponential smoothing method over single exponential is it ability to
generate multiple-ahead-forecast. Let:
St be the exponentially smoothed value of Yt at time t
S’t be the double exponentially smoothed value of Yt at time t
Computes the single exponentially smoothed value:
St = αYt + (1 – α)St-1
……………………….(2)
Computes the double exponentially smoothed value:
S’t = αSt + (1 – α)S’t-1 ……………………….(3)
Next,
𝑎𝑡 = 2St – S’t
And, computes the adjustment factors:
𝑏𝑡 =
α
1−α
(𝑆𝑡 − 𝑆 ′ 𝑡 )
Forecast for m-step-ahead are computed using the equation:
𝐹𝑡+𝑚 = 𝑎𝑡 + 𝑏𝑡 𝑚 ………………….(4)
As in exponential modeling, the main difficulty encountered when using this method is
the determination of the size α. As usual, the criterion is to choose α such that the MSD is
minimum. Again, solver used to solve this problem [8] .
3 Forecasting Performance Measures [5] [7]

Mean Forecast Error (MFE or Bias): Measures average deviation of forecast from actual.
MFE 

1 n
 ( At  Ft )
n t 1
……………(5)
Mean Absolute Deviation (MAD): Measures average absolute deviation of forecast from
actual
MAD 

1 n
 At  Ft
n t 1
………………(6)
Mean Absolute Percentage Error (MAPE): Measures absolute error as a percentage of
the forecast.
MAPE 

100 n At  Ft

n t 1 At
……………..(7)
Standard Squared Error (MSE): Measures variance of forecast error
MSE 
1 n
( At  Ft ) 2

n t 1
………………(8)
4 Analysis the data:
In this research, asthma disease data was used. The data was obtained from the
hospital in Sulaimaniyah governorate. A monthly data set for 7 years period (2005 to 2011)
is used and the data are shown in the figure below: 2500
2000
1500
Male
1000
Female
500
0
2005 2006 2007 2008 2009 2010 2011
Figure (1): Show the numbers of people infected with the asthma disease during the year
(2005-2011)
First: We draw the curve of the number of people infected with asthma during the year (20052011) .The horizontal axis for time and the vertical axis value of numbers of (male, female)
patients with asthma disease.
140
120
Male
100
80
60
40
20
0
Index
10
20
30
40
50
60
70
80
Figure (2) : The time series of the number of male patients infected with asthma disease during
the years (2005-2011)
Female
250
150
50
Index
10
20
30
40
50
60
70
80
Figure (3): The time series of the number of female patients infected with asthma disease during
the years (2005-2011)
Second: We are finding the values of the measurements (MAPE,MAD,MSD ) for the two models
below and according to the data the males infected with this type of disease:
Table (1): show the measures of the two models
Model
α
γ
MAPE
Single Exponential
0.1
-
44.211 16.136 447.846
MAD
MSD
Double Exponential 0.2 0.2 42.001 15.137 355.747
140
120
Male
100
80
60
40
20
0
1
8
16
24
32
40
48
Index
56
64
72
80
Figure (4): Show Smoothing Plot for Male (Single Exponential Smoothing)
140
120
Male
100
80
60
40
20
0
1
8
16
24
32
40
48
Index
56
64
72
80
Figure (5): Show Smoothing Plot for Male (Double Exponential Smoothing)
Through the table (1) we comparison between the two models by the measures of (MAPE, MAD,
MSD).From the measures we note that the best model is double exponential smoothing model
because the values of measures (MAPE, MAD, MSD) be less than the measures of single
exponential smoothing model.
Table (2) : Show the prediction and confidence interval of the numbers of male patients infected
with asthma disease during the year (2012-2013)
Year
Period
1
2
3
4
5
6
2012
7
8
9
10
11
12
Forecasting
57.65
Lower
Upper
20.57
61.49
23.63
65.33
26.64
69.16
29.59
73.00
32.48
76.84
35.33
80.68
38.14
84.51
40.90
88.35
43.62
92.19
46.31
96.02
48.96
99.86
51.58
Year
Period
Forecasting
1
94.74
2
99.35
3
104.02
4
108.74
5
113.52
118.34
6
2013
7
123.21
8
128.13
9
133.08
10
138.07
11
143.09
12
148.14
Lower
Upper
103.70
54.18
153.22
107.53
56.74
158.33
111.37
59.29
163.46
115.21
61.81
168.61
119.05
64.30
173.79
122.88
66.78
178.98
126.72
69.24
184.20
130.56
71.69
189.43
134.39
74.12
194.67
138.23
76.53
199.94
142.07
78.93
205.21
145.91
81.31
210.50
Depending on the table above we note that the number of the people who infected with
the asthma disease in the governorate of Sulaymaniyah of the male patients are increased over the
years 2012, 2013 and this reason is due to lack of health awareness among the people and the
people who infected with this type of the disease are not revision a specialist doctor for the
purpose of taking the necessary treatment.
200
Male
150
100
50
0
1
11
22
33
44
55
Index
66
77
88
99
Figure (6): Show the prediction of the number of male patients infected with the asthma diseases
Third: We are finding the values of the measurements (MAPE,MAD,MSD ) for the two models
below and according to the data the female infected with this type of disease:
Table (3): Show the measures of the two models
Model
α
γ
MAPE MAD
Single Exponential
0.1
-
30.01
29.11 1477.37
28.62
26.51 1112.35
Double Exponential 0.2 0.2
MSD
250
Female
200
150
100
50
1
8
16
24
32
40
48
Index
56
64
72
80
Figure (7): Show Smoothing Plot for Female (Single Exponential Smoothing)
250
Female
200
150
100
50
1
8
16
24
32
40
48
Index
56
64
72
80
Figure (8): Show Smoothing Plot for Female (Double Exponential Smoothing)
Through the table (3) we comparison between the two models by the measures of (MAPE, MAD,
MSD).From the measures we note that the best model is double exponential smoothing model
because the values of measures (MAPE, MAD, MSD) be less than the measures of single
exponential smoothing model.
Table (4): Show the prediction and confidence interval of the numbers of Female patients infected
with asthma disease during the year (2012-2013)
Year
Period
Forecasting
1
123.40
58.45
2
130.59
64.28
3
Lower
137.77
4
70.01
144.96
75.65
Upper
Year
Period
Forecasting
Lower
Upper
188.35
1
209.66
122.93
296.39
196.89
2
216.85
127.89
305.80
205.54
3
224.03
132.81
315.26
214.28
4
231.22
137.69
324.75
5
152.15
81.19
223.11
5
238.41
142.54
334.29
6
159.34
86.65
232.03
6
245.60
147.34
343.85
241.03
7
252.79
152.12
353.45
2012
7
166.53
92.02
2013
8
173.72
97.33
250.10
8
259.98
156.87
363.08
9
180.90
102.57
259.24
9
267.16
161.59
372.74
268.45
10
274.35
166.28
382.42
281.54
170.95
392.13
288.73
175.60
401.86
10
188.09
107.74
11
195.28
112.85
277.71
11
12
202.47
117.91
287.02
12
Depending on the table above we note that the number of the people who infected with
the asthma disease in the governorate of Sulaymaniyah of the female patients are increased over
the years 2012, 2013 and this reason is due to lack of health awareness among the people and the
people who infected with this type of the disease are not revision a specialist doctor for the
purpose of taking the necessary treatment.
400
Female
300
200
100
0
1
11
22
33
44
55
Index
66
77
88
99
Figure (9): Show the prediction of the number of female patients infected with the asthma diseases
5 Conclusions & Recommendations:
5-1 Conclusions
Through this study, we get a set of conclusions and must be necessary mentioned as follows: 1) Through the data analysis we note that the appropriate model to predict the number of
males patients infected with asthma disease is double exponential smoothing model
2) The appropriate model to predict the number of female patients infected with asthma is
double exponential smoothing model
3) From the data analysis we see that the numbers of male and female patient infected with
asthma disease are increases during the year (2012-2013).
5-2 Recommendations:
There is a set of recommendations for this study and these recommendations are: - :
1) People with this type of disease must take care of them by the government and open more
health centers for a dangerous disease that affects the respiratory system to humans.
2) Provides more data and information by the health center for researchers to conduct more
research in this type of disease.
3) Using statistical measurements more accurate to analyze this type of disease.
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