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.

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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

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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

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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

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Variance - also in standard MATLAB

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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

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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

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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