Statistics Toolbox

Function Category List

The Statistics Toolbox provides several categories of functions.

The Statistics Toolbox's Main Categories of Functions
Probability Distributions	Parameter Estimation
	Cumulative Distribution Functions (cdf)
	Probability Density Functions (pdf)
	Inverse Cumulative Distribution Functions
	Random Number Generators
	Moments of Distribution Functions
Descriptive Statistics	Descriptive statistics for data samples
Statistical Plotting	Statistical plots
Statistical Process Control	Statistical Process Control
Cluster Analysis	Grouping items with similar characteristics into clusters
Linear Models	Fitting linear models to data
Nonlinear Regression	Fitting nonlinear regression models
Design of Experiments	Design of Experiments
Principal Components Analysis	Principal Components Analysis
Multivariate Statistics	Multivariate statistics
Hypothesis Tests	Statistical tests of hypotheses
Distribution Testing	Tests for fitting distributions to data
Nonparametric Testing	Nonparametric testing
File I/O	Reading data from and writing data to operating-system files
Demonstrations	Demonstrations
Data	Data for examples

The following tables list the functions in each of these specific areas. The first seven tables contain probability distribution functions. The remaining tables describe the other categories of functions.

Parameter Estimation
betafit	Parameter estimation for the beta distribution
betalike	Beta log-likelihood function
binofit	Parameter estimation for the binomial distribution
expfit	Parameter estimation for the exponential distribution
gamfit	Parameter estimation for the gamma distribution
gamlike	Gamma log-likelihood function
mle	Maximum likelihood estimation
normfit	Parameter estimation for the normal distribution
normlike	Normal log-likelihood function
poissfit	Parameter estimation for the Poisson distribution
raylfit	Rayleigh parameter estimation
unifit	Parameter estimation for the uniform distribution
weibfit	Weibull parameter estimation

Cumulative Distribution Functions (cdf)
betacdf	Beta cdf
binocdf	Binomial cdf
cdf	Parameterized cdf routine
chi2cdf	Chi-square cdf
expcdf	Exponential cdf
fcdf	F cdf
gamcdf	Gamma cdf
geocdf	Geometric cdf
hygecdf	Hypergeometric cdf
logncdf	Lognormal cdf
nbincdf	Negative binomial cdf
ncfcdf	Noncentral F cdf
nctcdf	Noncentral t cdf
ncx2cdf	Noncentral Chi-square cdf
normcdf	Normal (Gaussian) cdf
poisscdf	Poisson cdf
raylcdf	Rayleigh cdf
tcdf	Student's t cdf
unidcdf	Discrete uniform cdf
unifcdf	Continuous uniform cdf
weibcdf	Weibull cdf

Probability Density Functions (pdf)
betapdf	Beta pdf
binopdf	Binomial pdf
chi2pdf	Chi-square pdf
exppdf	Exponential pdf
fpdf	F pdf
gampdf	Gamma pdf
geopdf	Geometric pdf
hygepdf	Hypergeometric pdf
lognpdf	Lognormal pdf
nbinpdf	Negative binomial pdf
ncfpdf	Noncentral F pdf
nctpdf	Noncentral t pdf
ncx2pdf	Noncentral Chi-square pdf
normpdf	Normal (Gaussian) pdf
pdf	Parameterized pdf routine
poisspdf	Poisson pdf
raylpdf	Rayleigh pdf
tpdf	Student's t pdf
unidpdf	Discrete uniform pdf
unifpdf	Continuous uniform pdf
weibpdf	Weibull pdf

Inverse Cumulative Distribution Functions
betainv	Beta critical values
binoinv	Binomial critical values
chi2inv	Chi-square critical values
expinv	Exponential critical values
finv	F critical values
gaminv	Gamma critical values
geoinv	Geometric critical values
hygeinv	Hypergeometric critical values
icdf	Parameterized inverse distribution routine
logninv	Lognormal critical values
nbininv	Negative binomial critical values
ncfinv	Noncentral F critical values
nctinv	Noncentral t critical values
ncx2inv	Noncentral Chi-square critical values
norminv	Normal (Gaussian) critical values
poissinv	Poisson critical values
raylinv	Rayleigh critical values
tinv	Student's t critical values
unidinv	Discrete uniform critical values
unifinv	Continuous uniform critical values
weibinv	Weibull critical values

Random Number Generators
betarnd	Beta random numbers
binornd	Binomial random numbers
chi2rnd	Chi-square random numbers
exprnd	Exponential random numbers
frnd	F random numbers
gamrnd	Gamma random numbers
geornd	Geometric random numbers
hygernd	Hypergeometric random numbers
lognrnd	Lognormal random numbers
mvnrnd	Multivariate normal random numbers
mvtrnd	Multivariate t random numbers
nbinrnd	Negative binomial random numbers
ncfrnd	Noncentral F random numbers
nctrnd	Noncentral t random numbers
ncx2rnd	Noncentral Chi-square random numbers
normrnd	Normal (Gaussian) random numbers
poissrnd	Poisson random numbers
random	Parameterized random number routine
raylrnd	Rayleigh random numbers
trnd	Student's t random numbers
unidrnd	Discrete uniform random numbers
unifrnd	Continuous uniform random numbers
weibrnd	Weibull random numbers

Moments of Distribution Functions
betastat	Beta mean and variance
binostat	Binomial mean and variance
chi2stat	Chi-square mean and variance
expstat	Exponential mean and variance
fstat	F mean and variance
gamstat	Gamma mean and variance
geostat	Geometric mean and variance
hygestat	Hypergeometric mean and variance
lognstat	Lognormal mean and variance
nbinstat	Negative binomial mean and variance
ncfstat	Noncentral F mean and variance
nctstat	Noncentral t mean and variance
ncx2stat	Noncentral Chi-square mean and variance
normstat	Normal (Gaussian) mean and variance
poisstat	Poisson mean and variance
raylstat	Rayleigh mean and variance
tstat	Student's t mean and variance
unidstat	Discrete uniform mean and variance
unifstat	Continuous uniform mean and variance
weibstat	Weibull mean and variance

Descriptive Statistics
bootstrp	Bootstrap statistics for any function
corrcoef	Correlation coefficients (in MATLAB)
cov	Covariance matrix (in MATLAB)
crosstab	Cross tabulation
geomean	Geometric mean
grpstats	Summary statistics by group
harmmean	Harmonic mean
iqr	Interquartile range
kurtosis	Sample kurtosis
mad	Mean absolute deviation
mean	Arithmetic average (in MATLAB)
median	50th percentile (in MATLAB)
moment	Central moments of all orders
nanmax	Maximum ignoring missing data
nanmean	Average ignoring missing data
nanmedian	Median ignoring missing data
nanmin	Minimum ignoring missing data
nanstd	Standard deviation ignoring missing data
nansum	Sum ignoring missing data
prctile	Empirical percentiles of a sample
range	Sample range
skewness	Sample skewness
std	Standard deviation (in MATLAB)
tabulate	Frequency table
trimmean	Trimmed mean
var	Variance

Statistical Plotting
boxplot	Box plots
cdfplot	Plot of empirical cumulative distribution function
errorbar	Error bar plot
fsurfht	Interactive contour plot of a function
gline	Interactive line drawing
gname	Interactive point labeling
gplotmatrix	Matrix of scatter plots grouped by a common variable
gscatter	Scatter plot of two variables grouped by a third
lsline	Add least-squares fit line to plotted data
normplot	Normal probability plots
pareto	Pareto charts
qqplot	Quantile-Quantile plots
rcoplot	Regression case order plot
refcurve	Reference polynomial
refline	Reference line
surfht	Interactive interpolating contour plot
weibplot	Weibull plotting

Statistical Process Control
capable	Quality capability indices
capaplot	Plot of process capability
ewmaplot	Exponentially weighted moving average plot
histfit	Histogram and normal density curve
normspec	Plot normal density between limits
schart	Time plot of standard deviation
xbarplot	Time plot of means

Cluster Analysis
cluster	Create clusters from linkage output
clusterdata	Create clusters from a dataset
cophenet	Calculate the cophenetic correlation coefficient
dendrogram	Plot a hierarchical tree in a dendrogram graph
inconsistent	Calculate the inconsistency values of objects in a cluster hierarchy tree
linkage	Link objects in a dataset into a hierarchical tree of binary clusters
pdist	Calculate the pairwise distance between objects in a dataset
squareform	Reformat output of pdist function from vector to square matrix
zscore	Normalize a dataset before calculating the distance

Linear Models
anova1	One-way Analysis of Variance (ANOVA)
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 (nonparametric two-way anova)
glmfit	Generalized linear model fitting
kruskalwallis	Kruskal-Wallis test (nonparametric one-way anova)
leverage	Regression diagnostic
lscov	Regression given a covariance matrix (in MATLAB)
manova1	One-way multivariate analysis of variance
manovacluster	Draw clusters of group means for manova1
multcompare	Multiple comparisons of means and other estimates
polyconf	Polynomial prediction with confidence intervals
polyfit	Polynomial fitting (in MATLAB)
polyval	Polynomial prediction (in MATLAB)
rcoplot	Residuals case order plot
regress	Multiple linear regression
regstats	Regression diagnostics
ridge	Ridge regression
rstool	Response surface tool
robustfit	Robust regression model fitting
rstool	Multidimensional response surface visualization (RSM)
stepwise	Stepwise regression GUI
x2fx	Factor settings matrix (X) to design matrix (D)

Nonlinear Regression
nlinfit	Nonlinear least-squares fitting
nlintool	Prediction graph for nonlinear fits
nlparci	Confidence intervals on parameters
nlpredci	Confidence intervals for prediction
nnls	Nonnegative least squares (in MATLAB)

Design of Experiments
cordexch	D-optimal design using coordinate exchange
daugment	D-optimal augmentation of designs
dcovary	D-optimal design with fixed covariates
ff2n	Two-level full factorial designs
fracfact	Two-level fractional factorial design
fullfact	Mixed level full factorial designs
hadamard	Hadamard designs (in MATLAB)
rowexch	D-optimal design using row exchange

Principal Components Analysis
barttest	Bartlett's test
pcacov	PCA from covariance matrix
pcares	Residuals from PCA
princomp	PCA from raw data matrix

Multivariate Statistics
classify	Linear Discriminant Analysis
mahal	Mahalanobis distance
manova1	One-way multivariate analysis of variance
manovacluster	Draw clusters of group means for manova1

Hypothesis Tests
ranksum	Wilcoxon rank sum test
signrank	Wilcoxon signed rank test
signtest	Sign test for paired samples
ttest	One sample t-test
ttest2	Two sample t-test
ztest	Z-test

Distribution Testing
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

Nonparametric Testing
friedman	Friedman's test (nonparametric two-way anova)
kruskalwallis	Kruskal-Wallis test (nonparametric one-way anova)
ranksum	Wilcoxon rank sum test (independent samples)
signrank	Wilcoxon sign rank test (paired samples)
signtest	Sign test (paired samples)

File I/O
caseread	Read casenames from a file
casewrite	Write casenames from a string matrix to a file
tblread	Retrieve tabular data from the file system
tblwrite	Write data in tabular form to the file system
tdfread	Read in text and numeric data from tab-delimited file

Demonstrations
aoctool	Interactive tool for analysis of covariance
disttool	Interactive exploration of distribution functions
glmdemo	Generalized linear model slide show
randtool	Interactive random number generation
polytool	Interactive fitting of polynomial models
rsmdemo	Interactive process experimentation and analysis
robustdemo	Interactive tool to compare robust and least squares fits

Data
census.mat	U. S. Population 1790 to 1980
cities.mat	Names of U.S. metropolitan areas
discrim.mat	Classification data
gas.mat	Gasoline prices
hald.mat	Hald data
hogg.mat	Bacteria counts from milk shipments
lawdata.mat	GPA versus LSAT for 15 law schools
mileage.mat	Mileage data for three car models from two factories
moore.mat	Five factor - one response regression data
parts.mat	Dimensional runout on 36 circular parts
popcorn.mat	Data for popcorn example (anova2, friedman)
polydata.mat	Data for polytool demo
reaction.mat	Reaction kinetics data
sat.dat	ASCII data for tblread example

Reference

Alphabetical List of Functions