Appendix E
MATLAB Statistics Toolbox
The following tables list the functions that are available in the MATLAB
Statistics Toolbox, Version 3.0. This toolbox is available for purchase from
The MathWorks, Inc.
TABL
ABLE E.1
Functions for Parameter Estimation (fit) and Distribution Statistics Mean and Variance (stat)
Function
Purpose
betafit, betastat
Beta distribution.
binofit, binostat
Binomial distribution.
expfit, expstat
fstat
gamfit, gamstat
geostat
Exponential distribution.
F distribution
Gamma distribution.
Geometric distribution
hygestat
Hypergeometric distribution
lognstat
Lognormal distribution
mle
nbinstat
Maximum likelihood parameter estimation.
Negative binomial distribution
ncfstat
Noncentral F distribution
nctstat
Noncentral t distribution
ncx2stat
Noncentral Chi-square distribution
normfit, normstat
Normal distribution.
poissfit, poisstat
Poisson distribution.
raylfit
Rayleigh distribution.
tstat
unidstat
T distribution
Discrete uniform distribution
unifit, unifstat
Uniform distribution.
weibfit, weibstat
Weibull distribution.
© 2002 by Chapman & Hall/CRC
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Computational Statistics Handbook with MATLAB
TABLE E.2
Probability Density Functions (pdf) and Cumulative Distribution
Functions (cdf)
Function
Purpose
betapdf, betacdf
Beta distribution
binopdf, binocdf
Binomial distribution
chi2pdf, chi2cdf
Chi-square distribution
exppdf, expcdf
Exponential distribution
fpdf, fcdf
F distribution
gampdf, gamcdf
Gamma distribution
geopdf, geocdf
Geometric distribution
hygepdf, hygecdf
Hypergeometric distribution
lognpdf, logncdf
Log normal distribution
nbinpdf, nbincdf
Negative binomial distribution
ncfpdf, ncfcdf
Noncentral F distribution
nctpdf, nctcdf
Noncentral t distribution
ncx2pdf, ncx2cdf
Noncentral chi-square distribution
normpdf, normcdf
Normal distribution
pdf, cdf
Probability density/Cumulative distribution
poisspdf, poisscdf
Poisson distribution
raylpdf, raylcdf
Rayleigh distribution
tpdf, tcdf
T distribution
unidpdf, unidcdf
Discrete uniform distribution
unifpdf, unifcdf
Continuous uniform distribution
weibpdf, weibcdf
Weibull distribution
© 2002 by Chapman & Hall/CRC
Appendix E: MATLAB Statistics Toolbox
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TABLE E.3
Critical Values (inv) and Random Number Generation (rnd) for
Probability Distribution Functions
Function
Purpose
betainv, betarnd
Beta distribution
binoinv, binornd
Binomial distribution
chi2inv, chi2rnd
Chi-square distribution
expinv, exprnd
Exponential distribution
finv, frnd
F distribution
gaminv, gamrnd
Gamma distribution
geoinv, geornd
Geometric distribution
hygeinv, hygernd
Hypergeometric distribution
logninv, lognrnd
Log normal distribution
nbininv, nbinrnd
Negative binomial distribution
ncfinv, ncfrnd
Noncentral F distribution
nctinv, nctrnd
Noncentral t distribution
ncx2inv, ncx2rnd
Noncentral chi-square distribution
norminv, normrnd
Normal distribution
poissinv, poissrnd
Poisson distribution
raylinv, raylrnd
Rayleigh distribution
tinv, trnd
T distribution
unidinv, unidrnd
Discrete uniform distribution
unifinv, unifrnd
Continuous uniform distribution
weibinv, weibrnd
Weibull distribution
icdf
Specified inverse cdf
© 2002 by Chapman & Hall/CRC
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Computational Statistics Handbook with MATLAB
TABLE E.4
Descriptive Statistics
Function
Purpose
bootstrp
Bootstrap statistics for any function.
corrcoef
Correlation coefficient - also in standard
MATLAB
cov
Covariance - also in standard MATLAB
crosstab
Cross tabulation
geomean
Geometric mean
grpstats
Summary statistics by group
harmmean
Harmonic mean
iqr
kurtosis
mad
mean
Interquartile range
Kurtosis
Median absolute deviation
Sample average - also in standard MATLAB
median
Second quartile (50th percentile) of a sample - also
in standard MATLAB
moment
Moments of a sample
nanmax, nanmin
nanmean, nanmedian
nanstd, namsum
prctile
range
skewness
std
Maximum/minimum - ignoring NaNs
Mean/median - ignoring NaNs
Standard deviation/sum - ignoring NaNs
Percentiles
Range
Skewness
Standard deviation - also in standard MATLAB
tabulate
Frequency table
trimmean
Trimmed mean
var
© 2002 by Chapman & Hall/CRC
Variance - also in standard MATLAB
Appendix E: MATLAB Statistics Toolbox
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TABLE E.5
Linear Models
Function
Purpose
anova1
One-way analysis of variance
anova2
Two-way analysis of variance
anovan
n-way analysis of variance
aoctool
Interactive tool for analysis of covariance
dummyvar
Dummy-variable coding
friedman
Friedman’s test
glmfit
kruskalwallis
lscov
Generalized linear model fitting
Kruskal-Wallis test
Least-squares estimates with known covariance
matrix
manoval
One-way multivariate analysis of variance
manovacluster
Draw clusters of group means for manova1
multcompare
polyconf
Multiple comparisons of means and other
estimates
Polynomial evaluation and confidence interval
estimation
polyfit
Least-squares polynomial fitting- also in standard
MATLAB
polyval
Predicted values for polynomial functions- also
in standard MATLAB
rcoplot
Residuals case order plot
regress
Multivariate linear regression
regstats
ridge
robustfit
rstool
stepwise
x2fx
© 2002 by Chapman & Hall/CRC
Regression diagnostics
Ridge regression
Robust regression model fitting
Multidimensional response surface visualization
Interactive tool for stepwise regression
Factor setting matrix (x) to design matrix (fx)
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TABLE E.6
Nonlinear Models
Function
nlinfit
Purpose
Nonlinear least-squares data fitting (Newton’s
Method)
nlintool
Interactive graphical tool for prediction in
nonlinear models
nlpredci
Confidence intervals for prediction
nlparci
Confidence intervals for parameters
nnls
Non-negative least-squares
TABLE E.7
Cluster Analysis
Function
pdist
squareform
linkage
dendrogram
inconsistent
cophenet
cluster
clusterdata
© 2002 by Chapman & Hall/CRC
Purpose
Pairwise distance between observations
Square matrix formatted distance
Hierarchical cluster information
Generate dendrogram plot
Inconsistent values of a cluster tree
Cophenetic coefficient
Construct clusters from linkage output
Construct clusters from data
Appendix E: MATLAB Statistics Toolbox
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TABLE E.8
Design of Experiments (DOE) and Statistical Process Control (SPC)
Function
Purpose
cordexch
D-optimal design (coordinate exchange
algorithm)
daugment
Augment D-optimal design
dcovary
ff2n
D-optimal design with fixed covariates
Two-level full-factorial design
fracfact
Two-level fractional factorial design
fullfact
Mixed-level full-factorial design
hadamarad
Hadamard matrices (orthogonal arrays)
rowexch
D-optimal (row exchange algorithm)
capable
Capability indices
capaplot
Capability plot
ewmaplot
Exponentially weighted moving average plot
histfit
Histogram with superimposed normal density
normspec
schart
xbarplot
Plot normal density between specification limits
S chart for monitoring variability
Xbar chart for monitoring the mean
TABLE E.9
Multivariate Statistics and Principal Component Analysis
Function
classify
mahal
manova1
barttest
Purpose
Linear discriminant analysis
Mahalanobis distance
One-way multivariate analysis of variance
Bartlett’s test for dimensionality
pcacov
Principal components from covariance matrix
pcares
Residuals from principal components
princomp
© 2002 by Chapman & Hall/CRC
Principal component analysis from raw data
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TABLE E.1
E.10
Hypothesis Tests
Function
ranksum
Purpose
Wilcoxon rank sum test (independent samples)
signrank
Wilcoxon sign rank test (paired samples)
signtest
Sign test (paired samples)
ztest
Z test
ttest
One sample t test
ttest2
Two sample t test
jbtest
Jarque-Bera test of normality
kstest
Kolmogorov-Smirnov test for one sample
kstest2
Kolmogorov-Smirnov test for two samples
lillietest
Lilliefors test of normality
TABLE E.1
E.11
Statistical Plotting
Function
Purpose
cdfplot
Plot of empirical cumulative distribution function
fsurfht
Interactive contour plot of a function
gline
Point, drag and click line drawing on figures
gname
Interactive point labeling in x-y plots
gplotmatrix
gscatter
lsline
normplot
qqplot
refcurve
refline
surfht
weibplot
© 2002 by Chapman & Hall/CRC
Matrix of scatter plots grouped by a common
variable
Scatter plot of two variables grouped by a third
Add least-square fit line to scatter plot
Normal probability plot
Quantile-quantile plot
Reference polynomial curve
Reference line
Interactive contour plot of a data grid
Weibull probability plot
Appendix E: MATLAB Statistics Toolbox
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TABLE E.1
E.12
Statistics Demos
Function
aoctool
disttool
glmdemo
Purpose
Interactive tool for analysis of covariance
GUI tool for exploring probability distribution
functions
Generalized linear model slide show
polytool
Interactive graph for prediction of fitted
polynomials
randtool
GUI tool for generating random numbers
rsmdemo
robustdemo
Reaction simulation
Interactive tool to compare robust and least
squares fits
TABLE E.1
E.13
File-based I/O
Function
tblread
tblwrite
tdfread
caseread
casewrite
© 2002 by Chapman & Hall/CRC
Purpose
Read in data in tabular format
Write out data in tabular format in file
Read in text and numeric data from tab-delimited
file
Read in case names
Write out case names to file