Documentation

Statistics and Machine Learning Toolbox Functions

Exploratory Data Analysis

Data Import and Export

dataset Arrays for statistical data
caseread Read case names from file
casewrite Write case names to file
export Write dataset array to file
tblread Read tabular data from file
tblwrite Write tabular data to file
tdfread Read tab-delimited file
xlsread Read Microsoft Excel spreadsheet file
xptread Create table from data stored in SAS XPORT format file

Data Types

Categorical Arrays

nominal Create nominal array
ordinal Create ordinal array
dummyvar Create dummy variables
grpstats Summary statistics organized by group
gplotmatrix Matrix of scatter plots by group
grp2idx Create index vector from grouping variable
gscatter Scatter plot by group
nominal Arrays for nominal data
ordinal Arrays for ordinal data

Dataset Arrays for Heterogeneous Data

dataset Arrays for statistical data
mat2dataset Convert matrix to dataset array
cell2dataset Convert cell array to dataset array
struct2dataset Convert structure array to dataset array
table2dataset Convert table to dataset array
dataset2cell Convert dataset array to cell array
dataset2struct Convert dataset array to structure
dataset2table Convert dataset array to table
export Write dataset array to file
grpstats Summary statistics organized by group
ismissing Find dataset array elements with missing values
join Merge observations

Descriptive Statistics

Summary Statistics

geomean Geometric mean
harmmean Harmonic mean
trimmean Mean excluding outliers
range Range of values
iqr Interquartile range
mad Mean or median absolute deviation
prctile Percentiles of a data set
quantile Quantiles of a data set
zscore Standardized z-scores
moment Central moments
skewness Skewness
kurtosis Kurtosis
corr Linear or rank correlation
cholcov Cholesky-like covariance decomposition
corrcov Convert covariance matrix to correlation matrix
partialcorr Linear or rank partial correlation coefficients
partialcorri Partial correlation coefficients adjusted for internal variables
grpstats Summary statistics organized by group
tabulate Frequency table
crosstab Cross-tabulation
tiedrank Rank adjusted for ties

Summary Statistics for Data with Missing Values

nancov Covariance ignoring NaN values
nanmax Maximum ignoring NaN values
nanmean Mean ignoring NaN values
nanmedian Median ignoring NaN values
nanmin Minimum ignoring NaN values
nanstd Standard deviation ignoring NaN values
nansum Sum ignoring NaN values
nanvar Variance, ignoring NaN values

Statistical Visualization

Univariate Plots

boxplot Box plot
cdfplot Empirical cumulative distribution function plot
dfittool Open Distribution Fitting app
disttool Interactive density and distribution plots
ecdfhist Histogram based on empirical cumulative distribution function
histfit Histogram with a distribution fit
normplot Normal probability plot
normspec Normal density plot between specifications
probplot Probability plots
qqplot Quantile-quantile plot
randtool Interactive random number generation
wblplot Weibull probability plot

Bivariate and Multivariate Plots

boxplot Box plot
gline Interactively add line to plot
gname Add case names to plot
gplotmatrix Matrix of scatter plots by group
gscatter Scatter plot by group
hist3 Bivariate histogram
lsline Add least-squares line to scatter plot
refcurve Add reference curve to plot
refline Add reference line to plot
scatterhist Scatter plot with marginal histograms

Cluster Analysis

Hierarchical Clustering

cluster Construct agglomerative clusters from linkages
clusterdata Agglomerative clusters from data
cophenet Cophenetic correlation coefficient
inconsistent Inconsistency coefficient
linkage Agglomerative hierarchical cluster tree
pdist Pairwise distance between pairs of objects
sequentialfs Sequential feature selection
squareform Format distance matrix

k-Means and k-Medoids Clustering

kmeans k-means clustering
kmedoids k-medoids clustering

Cluster Plots

dendrogram Dendrogram plot
optimalleaforder Optimal leaf ordering for hierarchical clustering
manovacluster Dendrogram of group mean clusters following MANOVA
silhouette Silhouette plot

Cluster Evaluation

clustering.evaluation.CalinskiHarabaszEvaluation Calinski-Harabasz criterion clustering evaluation object
clustering.evaluation.DaviesBouldinEvaluation Davies-Bouldin criterion clustering evaluation object
clustering.evaluation.GapEvaluation Gap criterion clustering evaluation object
clustering.evaluation.SilhouetteEvaluation Silhouette criterion clustering evaluation object
evalclusters Evaluate clustering solutions
addK Evaluate additional numbers of clusters
compact Compact clustering evaluation object
increaseB Increase reference data sets
plot Plot clustering evaluation object criterion values

Gaussian Mixture Models

fitgmdist Fit Gaussian mixture distribution to data
cluster Construct clusters from Gaussian mixture distribution
posterior Posterior probabilities of components
gmdistribution Gaussian mixture models

Probability Distributions

Discrete Distributions

Binomial Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
binocdf Binomial cumulative distribution function
binopdf Binomial probability density function
binoinv Binomial inverse cumulative distribution function
binostat Binomial mean and variance
binofit Binomial parameter estimates
binornd Binomial random numbers
random Random numbers
BinomialDistribution Binomial probability distribution object

Geometric Distribution

geocdf Geometric cumulative distribution function
geopdf Geometric probability density function
geoinv Geometric inverse cumulative distribution function
geostat Geometric mean and variance
geornd Geometric random numbers
random Random numbers

Hypergeometric Distribution

hygecdf Hypergeometric cumulative distribution function
hygepdf Hypergeometric probability density function
hygeinv Hypergeometric inverse cumulative distribution function
hygestat Hypergeometric mean and variance
hygernd Hypergeometric random numbers
random Random numbers

Multinomial Distribution

makedist Create probability distribution object
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
pdf Probability density functions
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
mnpdf Multinomial probability density function
mnrnd Multinomial random numbers
MultinomialDistribution Multinomial probability distribution object

Negative Binomial Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
nbincdf Negative binomial cumulative distribution function
nbinpdf Negative binomial probability density function
nbininv Negative binomial inverse cumulative distribution function
nbinstat Negative binomial mean and variance
nbinfit Negative binomial parameter estimates
nbinrnd Negative binomial random numbers
random Random numbers
NegativeBinomialDistribution Negative binomial distribution object

Poisson Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
poisscdf Poisson cumulative distribution function
poisspdf Poisson probability density function
poissinv Poisson inverse cumulative distribution function
poisstat Poisson mean and variance
poissfit Poisson parameter estimates
poissrnd Poisson random numbers
random Random numbers
PoissonDistribution Poisson probability distribution object

Uniform Distribution (Discrete)

unidcdf Discrete uniform cumulative distribution function
unidpdf Discrete uniform probability density function
unidinv Discrete uniform inverse cumulative distribution function
unidstat Discrete uniform mean and variance
unidrnd Discrete uniform random numbers
random Random numbers

Continuous Distributions

Beta Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
betacdf Beta cumulative distribution function
betapdf Beta probability density function
betainv Beta inverse cumulative distribution function
betalike Beta negative log-likelihood
betastat Beta mean and variance
betafit Beta parameter estimates
betarnd Beta random numbers
random Random numbers
BetaDistribution Beta probability distribution object

Birnbaum-Saunders Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
random Random numbers
BirnbaumSaundersDistribution Birnbaum-Saunders probability distribution object

Burr Type XII Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
pdf Probability density functions
random Random numbers
BurrDistribution Burr probability distribution object

Chi-Square Distribution

chi2cdf Chi-square cumulative distribution function
chi2pdf Chi-square probability density function
chi2inv Chi-square inverse cumulative distribution function
chi2stat Chi-square mean and variance
chi2gof Chi-square goodness-of-fit test
chi2rnd Chi-square random numbers
random Random numbers

Exponential Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
expcdf Exponential cumulative distribution function
exppdf Exponential probability density function
expinv Exponential inverse cumulative distribution function
explike Exponential negative log-likelihood
expstat Exponential mean and variance
expfit Exponential parameter estimates
exprnd Exponential random numbers
random Random numbers
ExponentialDistribution Exponential probability distribution object

Extreme Value Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
evcdf Extreme value cumulative distribution function
evpdf Extreme value probability density function
evinv Extreme value inverse cumulative distribution function
evlike Extreme value negative log-likelihood
evstat Extreme value mean and variance
evfit Extreme value parameter estimates
evrnd Extreme value random numbers
random Random numbers
ExtremeValueDistribution Extreme value probability distribution object

F Distribution

fcdf F cumulative distribution function
fpdf F probability density function
finv F inverse cumulative distribution function
fstat F mean and variance
frnd F random numbers
random Random numbers

Gamma Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
gamcdf Gamma cumulative distribution function
gampdf Gamma probability density function
gaminv Gamma inverse cumulative distribution function
gamlike Gamma negative log-likelihood
gamstat Gamma mean and variance
gamfit Gamma parameter estimates
gamrnd Gamma random numbers
randg Gamma random numbers with unit scale
random Random numbers
GammaDistribution Gamma probability distribution object

Generalized Extreme Value Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
gevcdf Generalized extreme value cumulative distribution function
gevpdf Generalized extreme value probability density function
gevinv Generalized extreme value inverse cumulative distribution function
gevlike Generalized extreme value negative log-likelihood
gevstat Generalized extreme value mean and variance
gevfit Generalized extreme value parameter estimates
gevrnd Generalized extreme value random numbers
random Random numbers
GeneralizedExtremeValueDistribution Generalized extreme value probability distribution object

Gaussian Mixture Distribution

fitgmdist Fit Gaussian mixture distribution to data
gmdistribution Gaussian mixture models

Generalized Pareto Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
gpcdf Generalized Pareto cumulative distribution function
gppdf Generalized Pareto probability density function
gpinv Generalized Pareto inverse cumulative distribution function
gplike Generalized Pareto negative log-likelihood
gpstat Generalized Pareto mean and variance
gpfit Generalized Pareto parameter estimates
gprnd Generalized Pareto random numbers
random Random numbers
GeneralizedParetoDistribution Generalized Pareto probability distribution object

Inverse Gaussian Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
random Random numbers
InverseGaussianDistribution Inverse Gaussian probability distribution object

Kernel Distribution

fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
ksdensity Kernel smoothing function estimate
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
pdf Probability density functions
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
KernelDistribution Kernel probability distribution object

Logistic Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
LogisticDistribution Logistic probability distribution object

Loglogistic Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
LoglogisticDistribution Loglogistic probability distribution object

Lognormal Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
logncdf Lognormal cumulative distribution function
lognpdf Lognormal probability density function
logninv Lognormal inverse cumulative distribution function
lognlike Lognormal negative log-likelihood
lognstat Lognormal mean and variance
lognfit Lognormal parameter estimates
lognrnd Lognormal random numbers
random Random numbers
LognormalDistribution Lognormal probability distribution object

Nakagami Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
NakagamiDistribution Nakagami probability distribution object

Noncentral Chi-Square Distribution

ncx2cdf Noncentral chi-square cumulative distribution function
ncx2pdf Noncentral chi-square probability density function
ncx2inv Noncentral chi-square inverse cumulative distribution function
ncx2stat Noncentral chi-square mean and variance
ncx2rnd Noncentral chi-square random numbers
random Random numbers

Noncentral F Distribution

ncfcdf Noncentral F cumulative distribution function
ncfpdf Noncentral F probability density function
ncfinv Noncentral F inverse cumulative distribution function
ncfstat Noncentral F mean and variance
ncfrnd Noncentral F random numbers
random Random numbers

Noncentral t Distribution

nctcdf Noncentral t cumulative distribution function
nctpdf Noncentral t probability density function
nctinv Noncentral t inverse cumulative distribution function
nctstat Noncentral t mean and variance
nctrnd Noncentral t random numbers
random Random numbers

Normal Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
normcdf Normal cumulative distribution function
normpdf Normal probability density function
norminv Normal inverse cumulative distribution function
normlike Normal negative log-likelihood
normstat Normal mean and variance
normfit Normal parameter estimates
normrnd Normal random numbers
random Random numbers
NormalDistribution Normal probability distribution object

Piecewise Linear Distribution

makedist Create probability distribution object
paretotails Empirical distributions with Pareto tails
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
pdf Probability density functions
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
PiecewiseLinearDistribution Piecewise linear probability distribution object

Rayleigh Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
raylcdf Rayleigh cumulative distribution function
raylpdf Rayleigh probability density function
raylinv Rayleigh inverse cumulative distribution function
raylstat Rayleigh mean and variance
raylfit Rayleigh parameter estimates
raylrnd Rayleigh random numbers
random Random numbers
RayleighDistribution Rayleigh probability distribution object

Rician Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
RicianDistribution Rician probability distribution object

Student's t Distribution

tcdf Student's t cumulative distribution function
tpdf Student's t probability density function
tinv Student's t inverse cumulative distribution function
tstat Student's t mean and variance
trnd Student's t random numbers
random Random numbers

t Location-Scale Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
cdf Cumulative distribution functions
dfittool Open Distribution Fitting app
icdf Inverse cumulative distribution functions
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
pdf Probability density functions
tLocationScaleDistribution t Location-Scale probability distribution object

Triangular Distribution

makedist Create probability distribution object
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
pdf Probability density functions
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
TriangularDistribution Triangular probability distribution object

Uniform Distribution (Continuous)

makedist Create probability distribution object
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
pdf Probability density functions
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
unifcdf Continuous uniform cumulative distribution function
unifpdf Continuous uniform probability density function
unifinv Continuous uniform inverse cumulative distribution function
unifit Continuous uniform parameter estimates
unifstat Continuous uniform mean and variance
unifrnd Continuous uniform random numbers
random Random numbers
UniformDistribution Uniform probability distribution object

Weibull Distribution

makedist Create probability distribution object
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
cdf Cumulative distribution functions
icdf Inverse cumulative distribution functions
iqr Interquartile range
mean Mean of probability distribution
median Median of probability distribution
negloglik Negative log likelihood of probability distribution
paramci Confidence intervals for probability distribution parameters
pdf Probability density functions
proflik Profile likelihood function for probability distribution
random Random numbers
std Standard deviation of probability distribution
truncate Truncate probability distribution object
var Variance of probability distribution
wblcdf Weibull cumulative distribution function
wblpdf Weibull probability density function
wblinv Weibull inverse cumulative distribution function
wbllike Weibull negative log-likelihood
wblstat Weibull mean and variance
wblfit Weibull parameter estimates
wblrnd Weibull random numbers
random Random numbers
WeibullDistribution Weibull probability distribution object

Multivariate Distributions

Copula Distributions and Correlated Samples

copulacdf Copula cumulative distribution function
copulapdf Copula probability density function
copulaparam Copula parameters as function of rank correlation
copulastat Copula rank correlation
copulafit Fit copula to data
copularnd Copula random numbers

Inverse Wishart Distribution

iwishrnd Inverse Wishart random numbers

Multivariate Normal Distribution

mvncdf Multivariate normal cumulative distribution function
mvnpdf Multivariate normal probability density function
mvnrnd Multivariate normal random numbers

Multivariate t Distribution

mvtcdf Multivariate t cumulative distribution function
mvtpdf Multivariate t probability density function
mvtrnd Multivariate t random numbers

Wishart Distribution

wishrnd Wishart random numbers

Exploration and Visualization

dfittool Open Distribution Fitting app
disttool Interactive density and distribution plots
fsurfht Interactive contour plot
randtool Interactive random number generation
surfht Interactive contour plot
boxplot Box plot
cdfplot Empirical cumulative distribution function plot
ecdf Empirical cumulative distribution function
ecdfhist Histogram based on empirical cumulative distribution function
hist3 Bivariate histogram
histfit Histogram with a distribution fit
ksdensity Kernel smoothing function estimate
normplot Normal probability plot
normspec Normal density plot between specifications
probplot Probability plots
qqplot Quantile-quantile plot
scatterhist Scatter plot with marginal histograms
wblplot Weibull probability plot

Pseudorandom and Quasirandom Number Generation

Markov Chain Samplers

slicesample Slice sampler
mhsample Metropolis-Hastings sample

Flexible Distribution Families

pearsrnd Pearson system random numbers
johnsrnd Johnson system random numbers

Quasirandom Numbers

haltonset Halton quasi-random point sets
qrandset Quasi-random point sets
qrandstream Quasi-random number streams
sobolset Sobol quasi-random point sets

Resampling Techniques

bootci Bootstrap confidence interval
bootstrp Bootstrap sampling
combnk Enumeration of combinations
crossval Loss estimate using cross validation
datasample Randomly sample from data, with or without replacement
jackknife Jackknife sampling
randsample Random sample

Hypothesis Tests

Distribution Tests

adtest Anderson-Darling test
chi2gof Chi-square goodness-of-fit test
crosstab Cross-tabulation
dwtest Durbin-Watson test
fishertest Fisher's exact test
jbtest Jarque-Bera test
kstest One-sample Kolmogorov-Smirnov test
kstest2 Two-sample Kolmogorov-Smirnov test
lillietest Lilliefors test
runstest Run test for randomness

Location Tests

crosstab Cross-tabulation
fishertest Fisher's exact test
friedman Friedman's test
kruskalwallis Kruskal-Wallis test
multcompare Multiple comparison test
ranksum Wilcoxon rank sum test
sampsizepwr Sample size and power of test
signrank Wilcoxon signed rank test
signtest Sign test
ttest One-sample and paired-sample t-test
ttest2 Two-sample t-test
ztest z-test

Dispersion Tests

ansaribradley Ansari-Bradley test
barttest Bartlett's test
sampsizepwr Sample size and power of test
vartest Chi-square variance test
vartest2 Two-sample F-test for equal variances
vartestn Multiple-sample tests for equal variances

Regression and ANOVA

Linear Regression

Multiple Linear Regression

LinearModel Linear regression model class
fitlm Create linear regression model
stepwiselm Create linear regression model using stepwise regression
disp Display linear regression model
feval Evaluate linear regression model prediction
predict Predict response of linear regression model
random Simulate responses for linear regression model
plot Scatter plot or added variable plot of linear model
plotAdjustedResponse Adjusted response plot for linear regression model
dummyvar Create dummy variables
invpred Inverse prediction
plsregress Partial least-squares regression
x2fx Convert predictor matrix to design matrix
relieff Importance of attributes (predictors) using ReliefF algorithm
regress Multiple linear regression
robustdemo Interactive robust regression
robustfit Robust regression
rsmdemo Interactive response surface demonstration
rstool Interactive response surface modeling

Stepwise Regression

LinearModel Linear regression model class
stepwiselm Create linear regression model using stepwise regression
fitlm Create linear regression model
addTerms Add terms to linear regression model
removeTerms Remove terms from linear model
step Improve linear regression model by adding or removing terms
stepwise Interactive stepwise regression
stepwisefit Stepwise regression

Multivariate Regression

mvregress Multivariate linear regression
mvregresslike Negative log-likelihood for multivariate regression
polytool Interactive polynomial fitting
polyconf Polynomial confidence intervals

Regularization

lasso Regularized least-squares regression using lasso or elastic net algorithms
ridge Ridge regression
lassoPlot Trace plot of lasso fit

Mixed Effects

LinearMixedModel Linear mixed-effects model class
fitlme Fit linear mixed-effects model
fitlmematrix Fit linear mixed-effects model
disp Display linear mixed-effects model
predict Predict response of linear mixed-effects model
random Generate random responses from fitted linear mixed-effects model
fixedEffects Estimates of fixed effects and related statistics
randomEffects Estimates of random effects and related statistics
designMatrix Fixed- and random-effects design matrices
fitted Fitted responses from a linear mixed-effects model
response Response vector of the linear mixed-effects model
anova Analysis of variance for linear mixed-effects model
coefCI Confidence intervals for coefficients of linear mixed-effects model
coefTest Hypothesis test on fixed and random effects of linear mixed-effects model
compare Compare linear mixed-effects models
covarianceParameters Extract covariance parameters of linear mixed-effects model
plotResiduals Plot residuals of linear mixed-effects model
residuals Residuals of fitted linear mixed-effects model

Model Assessment

LinearModel Linear regression model class
fitlm Create linear regression model
stepwiselm Create linear regression model using stepwise regression
anova Analysis of variance for linear model
coefCI Confidence intervals of coefficient estimates of linear model
coefTest Linear hypothesis test on linear regression model coefficients
dwtest Durbin-Watson test of linear model
plot Scatter plot or added variable plot of linear model
plotAdded Added variable plot or leverage plot for linear model
plotAdjustedResponse Adjusted response plot for linear regression model
plotDiagnostics Plot diagnostics of linear regression model
plotEffects Plot main effects of each predictor in linear regression model
plotInteraction Plot interaction effects of two predictors in linear regression model
plotResiduals Plot residuals of linear regression model
plotSlice Plot of slices through fitted linear regression surface
leverage Leverage
regstats Regression diagnostics
addedvarplot Added variable plot
gline Interactively add line to plot
lsline Add least-squares line to scatter plot
rcoplot Residual case order plot
refcurve Add reference curve to plot
refline Add reference line to plot
linhyptest Linear hypothesis test

Generalized Linear Models

Generalized Linear Regression

GeneralizedLinearModel Generalized linear regression model class
fitglm Create generalized linear regression model
stepwiseglm Create generalized linear regression model by stepwise regression
disp Display generalized linear regression model
feval Evaluate generalized linear regression model prediction
predict Predict response of generalized linear regression model
random Simulate responses for generalized linear regression model
mnrfit Multinomial logistic regression
mnrval Multinomial logistic regression values
glmfit Generalized linear model regression
glmval Generalized linear model values

Stepwise Regression

GeneralizedLinearModel Generalized linear regression model class
stepwiseglm Create generalized linear regression model by stepwise regression
fitglm Create generalized linear regression model
addTerms Add terms to generalized linear model
removeTerms Remove terms from generalized linear model
step Improve generalized linear regression model by adding or removing terms

Regularization

lassoglm Lasso or elastic net regularization for generalized linear model regression

Mixed Effects

GeneralizedLinearMixedModel Generalized linear mixed-effects model class
fitglme Fit generalized linear mixed-effects model
disp Display generalized linear mixed-effects model
predict Predict response of generalized linear mixed-effects model
random Generate random responses from fitted generalized linear mixed-effects model
fixedEffects Estimates of fixed effects and related statistics
randomEffects Estimates of random effects and related statistics
designMatrix Fixed- and random-effects design matrices
fitted Fitted responses from generalized linear mixed-effects model
response Response vector of generalized linear mixed-effects model
anova Analysis of variance for generalized linear mixed-effects model
coefCI Confidence intervals for coefficients of generalized linear mixed-effects model
coefTest Hypothesis test on fixed and random effects of generalized linear mixed-effects model
compare Compare generalized linear mixed-effects models
covarianceParameters Extract covariance parameters of generalized linear mixed-effects model
plotResiduals Plot residuals of generalized linear mixed-effects model
residuals Residuals of fitted generalized linear mixed-effects model
refit Refit generalized linear mixed-effects model

Model Assessment

GeneralizedLinearModel Generalized linear regression model class
fitglm Create generalized linear regression model
stepwiseglm Create generalized linear regression model by stepwise regression
coefCI Confidence intervals of coefficient estimates of generalized linear model
coefTest Linear hypothesis test on generalized linear regression model coefficients
devianceTest Analysis of deviance
plotDiagnostics Plot diagnostics of generalized linear regression model
plotResiduals Plot residuals of generalized linear regression model
plotSlice Plot of slices through fitted generalized linear regression surface
linhyptest Linear hypothesis test

Nonlinear Regression

Nonlinear Models

NonLinearModel Nonlinear regression model class
fitnlm Fit nonlinear regression model
disp Display nonlinear regression model
feval Evaluate nonlinear regression model prediction
predict Predict response of nonlinear regression model
random Simulate responses for nonlinear regression model
dummyvar Create dummy variables
hougen Hougen-Watson model
statset Create statistics options structure
statget Access values in statistics options structure
nlinfit Nonlinear regression
nlintool Interactive nonlinear regression
nlparci Nonlinear regression parameter confidence intervals
nlpredci Nonlinear regression prediction confidence intervals

Mixed Effects

nlmefit Nonlinear mixed-effects estimation
nlmefitsa Fit nonlinear mixed-effects model with stochastic EM algorithm

Model Assessment

NonLinearModel Nonlinear regression model class
fitnlm Fit nonlinear regression model
coefCI Confidence intervals of coefficient estimates of nonlinear regression model
coefTest Linear hypothesis test on nonlinear regression model coefficients
plotDiagnostics Plot diagnostics of nonlinear regression model
plotResiduals Plot residuals of nonlinear regression model
plotSlice Plot of slices through fitted nonlinear regression surface
linhyptest Linear hypothesis test

ANOVA

Analysis of Variance and Covariance

anova1 One-way analysis of variance
anova2 Two-way analysis of variance
anovan N-way analysis of variance
aoctool Interactive analysis of covariance
canoncorr Canonical correlation
dummyvar Create dummy variables
friedman Friedman's test
kruskalwallis Kruskal-Wallis test
multcompare Multiple comparison test

Repeated Measures and MANOVA

fitrm Fit repeated measures model
ranova Repeated measures analysis of variance
mauchly Mauchly's test for sphericity
epsilon Epsilon adjustment for repeated measures anova
multcompare Multiple comparison of estimated marginal means
anova Analysis of variance for between-subject effects
manova Multivariate analysis of variance
coeftest Linear hypothesis test on coefficients of repeated measures model
grpstats Compute descriptive statistics of repeated measures data by group
margmean Estimate marginal means
plot Plot data with optional grouping
plotprofile Plot expected marginal means with optional grouping
predict Compute predicted values given predictor values
random Generate new random response values given predictor values
manova1 One-way multivariate analysis of variance
manovacluster Dendrogram of group mean clusters following MANOVA
multcompare Multiple comparison test
RepeatedMeasuresModel Repeated measures model class

Machine Learning

Supervised Learning

Linear Regression

Multiple Linear Regression
LinearModel Linear regression model class
fitlm Create linear regression model
stepwiselm Create linear regression model using stepwise regression
disp Display linear regression model
feval Evaluate linear regression model prediction
predict Predict response of linear regression model
random Simulate responses for linear regression model
plot Scatter plot or added variable plot of linear model
plotAdjustedResponse Adjusted response plot for linear regression model
dummyvar Create dummy variables
invpred Inverse prediction
plsregress Partial least-squares regression
x2fx Convert predictor matrix to design matrix
relieff Importance of attributes (predictors) using ReliefF algorithm
regress Multiple linear regression
robustdemo Interactive robust regression
robustfit Robust regression
rsmdemo Interactive response surface demonstration
rstool Interactive response surface modeling
Stepwise Regression
LinearModel Linear regression model class
stepwiselm Create linear regression model using stepwise regression
fitlm Create linear regression model
addTerms Add terms to linear regression model
removeTerms Remove terms from linear model
step Improve linear regression model by adding or removing terms
stepwise Interactive stepwise regression
stepwisefit Stepwise regression
Multivariate Regression
mvregress Multivariate linear regression
mvregresslike Negative log-likelihood for multivariate regression
polytool Interactive polynomial fitting
polyconf Polynomial confidence intervals
Regularization
lasso Regularized least-squares regression using lasso or elastic net algorithms
ridge Ridge regression
lassoPlot Trace plot of lasso fit
Model Assessment
LinearModel Linear regression model class
fitlm Create linear regression model
stepwiselm Create linear regression model using stepwise regression
anova Analysis of variance for linear model
coefCI Confidence intervals of coefficient estimates of linear model
coefTest Linear hypothesis test on linear regression model coefficients
dwtest Durbin-Watson test of linear model
plot Scatter plot or added variable plot of linear model
plotAdded Added variable plot or leverage plot for linear model
plotAdjustedResponse Adjusted response plot for linear regression model
plotDiagnostics Plot diagnostics of linear regression model
plotEffects Plot main effects of each predictor in linear regression model
plotInteraction Plot interaction effects of two predictors in linear regression model
plotResiduals Plot residuals of linear regression model
plotSlice Plot of slices through fitted linear regression surface
leverage Leverage
regstats Regression diagnostics
addedvarplot Added variable plot
gline Interactively add line to plot
lsline Add least-squares line to scatter plot
rcoplot Residual case order plot
refcurve Add reference curve to plot
refline Add reference line to plot
linhyptest Linear hypothesis test

Nonlinear Regression

Nonlinear Models
NonLinearModel Nonlinear regression model class
fitnlm Fit nonlinear regression model
disp Display nonlinear regression model
feval Evaluate nonlinear regression model prediction
predict Predict response of nonlinear regression model
random Simulate responses for nonlinear regression model
dummyvar Create dummy variables
hougen Hougen-Watson model
statset Create statistics options structure
statget Access values in statistics options structure
nlinfit Nonlinear regression
nlintool Interactive nonlinear regression
nlparci Nonlinear regression parameter confidence intervals
nlpredci Nonlinear regression prediction confidence intervals
Model Assessment
NonLinearModel Nonlinear regression model class
NonLinearModel.fit Fit nonlinear regression model
coefCI Confidence intervals of coefficient estimates of nonlinear regression model
coefTest Linear hypothesis test on nonlinear regression model coefficients
plotDiagnostics Plot diagnostics of nonlinear regression model
plotResiduals Plot residuals of nonlinear regression model
plotSlice Plot of slices through fitted nonlinear regression surface
linhyptest Linear hypothesis test

Generalized Linear Models

Generalized Linear Regression
GeneralizedLinearModel Generalized linear regression model class
fitglm Create generalized linear regression model
stepwiseglm Create generalized linear regression model by stepwise regression
disp Display generalized linear regression model
feval Evaluate generalized linear regression model prediction
predict Predict response of generalized linear regression model
random Simulate responses for generalized linear regression model
mnrfit Multinomial logistic regression
mnrval Multinomial logistic regression values
glmfit Generalized linear model regression
glmval Generalized linear model values
Stepwise Regression
GeneralizedLinearModel Generalized linear regression model class
stepwiseglm Create generalized linear regression model by stepwise regression
fitglm Create generalized linear regression model
addTerms Add terms to generalized linear model
removeTerms Remove terms from generalized linear model
step Improve generalized linear regression model by adding or removing terms
Regularization
lassoglm Lasso or elastic net regularization for generalized linear model regression
Model Assessment
GeneralizedLinearModel Generalized linear regression model class
fitglm Create generalized linear regression model
stepwiseglm Create generalized linear regression model by stepwise regression
coefCI Confidence intervals of coefficient estimates of generalized linear model
coefTest Linear hypothesis test on generalized linear regression model coefficients
devianceTest Analysis of deviance
plotDiagnostics Plot diagnostics of generalized linear regression model
plotResiduals Plot residuals of generalized linear regression model
plotSlice Plot of slices through fitted generalized linear regression surface
linhyptest Linear hypothesis test

Classification Trees and Regression Trees

fitctree Fit classification tree
predict Predict classification
fitrtree Binary decision tree for regression
predict Predict response of regression tree
templateTree Create decision tree template
loss Classification error
view View tree
prune Produce sequence of subtrees by pruning
crossval Cross-validated decision tree
predictorImportance Estimates of predictor importance
loss Regression error
view View tree
prune Produce sequence of subtrees by pruning
crossval Cross-validated decision tree
predictorImportance Estimates of predictor importance
ClassificationTree Binary decision tree for classification
RegressionTree Regression tree
CompactClassificationTree Compact classification tree
ClassificationPartitionedModel Cross-validated classification model
CompactRegressionTree Compact regression tree
RegressionPartitionedModel Cross-validated regression model

Support Vector Machines

fitcsvm Train binary support vector machine classifier
predict Predict labels for support vector machine classifiers
templateSVM Support vector machine template
fitcecoc Fit multiclass models for support vector machines or other classifiers
templateECOC Error-correcting output codes learner template
predict Predict labels for error-correcting output code multiclass classifiers
fitSVMPosterior Fit posterior probabilities
loss Classification error for support vector machine classifiers
crossval Cross-validated support vector machine classifier
edge Classification edge for support vector machine classifiers
margin Classification margins for support vector machine classifiers
resume Resume training support vector machine classifier
loss Classification loss for error-correcting output code multiclass classifiers
crossval Cross-validated, error-correcting output code multiclass model
designecoc Coding matrix for reducing error-correcting output code to binary
ClassificationSVM Support vector machine for binary classification
ClassificationECOC Multiclass model for support vector machines or other classifiers
CompactClassificationSVM Compact support vector machine for binary classification
CompactClassificationECOC Compact multiclass model for support vector machines or other classifiers
ClassificationPartitionedModel Cross-validated classification model
ClassificationPartitionedECOC Cross-validated multiclass model for support vector machines or other classifiers

Discriminant Analysis

fitcdiscr Fit discriminant analysis classifier
predict Predict classification
templateDiscriminant Discriminant analysis classifier template
makecdiscr Construct discriminant analysis classifier from parameters
loss Classification error
crossval Cross-validated discriminant analysis classifier
cvshrink Cross-validate regularization of linear discriminant
logP Log unconditional probability density for discriminant analysis classifier
ClassificationDiscriminant Discriminant analysis classification
CompactClassificationDiscriminant Compact discriminant analysis class
ClassificationPartitionedModel Cross-validated classification model

Naive Bayes Classification

fitcnb Train multiclass naive Bayes model
predict Predict classification for naive Bayes models
templateNaiveBayes Naive Bayes classifier template
loss Classification error for naive Bayes classifier
crossval Cross-validated naive Bayes classifier
logP Log unconditional probability density for naive Bayes classifier
ClassificationNaiveBayes Naive Bayes classification
CompactClassificationNaiveBayes Compact naive Bayes classifier
ClassificationPartitionedModel Cross-validated classification model

Nearest Neighbors

fitcknn Fit k-nearest neighbor classifier
predict k-nearest neighbor classification
templateKNN k-nearest neighbor classifier template
loss k-nearest neighbor classification
crossval k-nearest neighbor classification
pdist Pairwise distance between pairs of objects
pdist2 Pairwise distance between two sets of observations
ExhaustiveSearcher Prepare exhaustive nearest neighbors searcher
KDTreeSearcher Grow Kd-tree
createns Create object to use in k-nearest neighbors search
ClassificationKNN k-nearest neighbor classification
ClassificationPartitionedModel Cross-validated classification model

Model Building and Assessment

sequentialfs Sequential feature selection
relieff Importance of attributes (predictors) using ReliefF algorithm
crossval Loss estimate using cross validation
confusionmat Confusion matrix
perfcurve Receiver operating characteristic (ROC) curve or other performance curve for classifier output
testcholdout Compare predictive accuracies of two classification models
testckfold Compare accuracies of two classification models by repeated cross validation
cvpartition Data partitions for cross validation

Unsupervised Learning

Hierarchical Clustering

cluster Construct agglomerative clusters from linkages
clusterdata Agglomerative clusters from data
cophenet Cophenetic correlation coefficient
inconsistent Inconsistency coefficient
linkage Agglomerative hierarchical cluster tree
pdist Pairwise distance between pairs of objects
sequentialfs Sequential feature selection
squareform Format distance matrix

k-Means and k-Medoids Clustering

kmeans k-means clustering
kmedoids k-medoids clustering

Nearest Neighbors

ExhaustiveSearcher Exhaustive nearest neighbors searcher
KDTreeSearcher Nearest neighbor search using Kd-tree
ExhaustiveSearcher Prepare exhaustive nearest neighbors searcher
KDTreeSearcher Grow Kd-tree
createns Create object to use in k-nearest neighbors search
knnsearch k-nearest neighbors search using Kd-tree or exhaustive search
rangesearch Find all neighbors within specified distance using exhaustive search or Kd-tree

Gaussian Mixture Models

fitgmdist Fit Gaussian mixture distribution to data
cluster Construct clusters from Gaussian mixture distribution
posterior Posterior probabilities of components
gmdistribution Gaussian mixture models

Hidden Markov Models

hmmdecode Hidden Markov model posterior state probabilities
hmmestimate Hidden Markov model parameter estimates from emissions and states
hmmgenerate Hidden Markov model states and emissions
hmmtrain Hidden Markov model parameter estimates from emissions
hmmviterbi Hidden Markov model most probable state path

Cluster Evaluation

clustering.evaluation.CalinskiHarabaszEvaluation Calinski-Harabasz criterion clustering evaluation object
clustering.evaluation.DaviesBouldinEvaluation Davies-Bouldin criterion clustering evaluation object
clustering.evaluation.GapEvaluation Gap criterion clustering evaluation object
clustering.evaluation.SilhouetteEvaluation Silhouette criterion clustering evaluation object
evalclusters Evaluate clustering solutions
addK Evaluate additional numbers of clusters
compact Compact clustering evaluation object
increaseB Increase reference data sets
plot Plot clustering evaluation object criterion values

Ensemble Learning

Boosting

fitensemble Fitted ensemble for classification or regression
templateEnsemble Ensemble learning template
predict Predict classification
predict Predict response of ensemble
fitcecoc Fit multiclass models for support vector machines or other classifiers
predict Predict labels for error-correcting output code multiclass classifiers
loss Classification error
crossval Cross validate ensemble
predictorImportance Estimates of predictor importance
resume Resume training ensemble
loss Regression error
crossval Cross validate ensemble
cvshrink Cross validate shrinking (pruning) ensemble
predictorImportance Estimates of predictor importance
resume Resume training ensemble
loss Classification loss for error-correcting output code multiclass classifiers
crossval Cross-validated, error-correcting output code multiclass model
ClassificationEnsemble Ensemble classifier
ClassificationECOC Multiclass model for support vector machines or other classifiers
RegressionEnsemble Ensemble regression
CompactClassificationEnsemble Compact classification ensemble class
ClassificationPartitionedEnsemble Cross-validated classification ensemble
CompactClassificationECOC Compact multiclass model for support vector machines or other classifiers
ClassificationPartitionedECOC Cross-validated multiclass model for support vector machines or other classifiers
CompactRegressionEnsemble Compact regression ensemble class
RegressionPartitionedEnsemble Cross-validated regression ensemble

Bagging

fitensemble Fitted ensemble for classification or regression
templateEnsemble Ensemble learning template
predict Predict classification
oobPredict Predict out-of-bag response of ensemble
predict Predict response of ensemble
oobPredict Predict out-of-bag response of ensemble
loss Classification error
crossval Cross validate ensemble
predictorImportance Estimates of predictor importance
resume Resume training ensemble
loss Regression error
crossval Cross validate ensemble
cvshrink Cross validate shrinking (pruning) ensemble
predictorImportance Estimates of predictor importance
resume Resume training ensemble
ClassificationBaggedEnsemble Classification ensemble grown by resampling
RegressionBaggedEnsemble Regression ensemble grown by resampling
CompactClassificationEnsemble Compact classification ensemble class
ClassificationPartitionedEnsemble Cross-validated classification ensemble
CompactRegressionEnsemble Compact regression ensemble class
RegressionPartitionedEnsemble Cross-validated regression ensemble
CompactTreeBagger Compact ensemble of decision trees grown by bootstrap aggregation
TreeBagger Names of classes

Random Subspace

fitensemble Fitted ensemble for classification or regression
templateEnsemble Ensemble learning template
predict Predict classification
loss Classification error
crossval Cross validate ensemble
predictorImportance Estimates of predictor importance
resume Resume training ensemble
loss Regression error
ClassificationEnsemble Ensemble classifier
CompactClassificationEnsemble Compact classification ensemble class
ClassificationPartitionedEnsemble Cross-validated classification ensemble

Multivariate Data Analysis

Multivariate Regression

mvregress Multivariate linear regression
mvregresslike Negative log-likelihood for multivariate regression
polytool Interactive polynomial fitting
polyconf Polynomial confidence intervals

Repeated Measures and MANOVA

fitrm Fit repeated measures model
ranova Repeated measures analysis of variance
mauchly Mauchly's test for sphericity
epsilon Epsilon adjustment for repeated measures anova
multcompare Multiple comparison of estimated marginal means
anova Analysis of variance for between-subject effects
manova Multivariate analysis of variance
coeftest Linear hypothesis test on coefficients of repeated measures model
grpstats Compute descriptive statistics of repeated measures data by group
margmean Estimate marginal means
plot Plot data with optional grouping
plotprofile Plot expected marginal means with optional grouping
predict Compute predicted values given predictor values
random Generate new random response values given predictor values
manova1 One-way multivariate analysis of variance
manovacluster Dendrogram of group mean clusters following MANOVA
multcompare Multiple comparison test
RepeatedMeasuresModel Repeated measures model class

Principal Component Analysis (PCA) and Canonical Correlation

barttest Bartlett's test
canoncorr Canonical correlation
pca Principal component analysis of raw data
pcacov Principal component analysis on covariance matrix
pcares Residuals from principal component analysis
ppca Probabilistic principal component analysis
rotatefactors Rotate factor loadings

Factor Analysis

factoran Factor analysis
rotatefactors Rotate factor loadings

Nonnegative Matrix Factorization

nnmf Nonnegative matrix factorization

Multidimensional Scaling

cmdscale Classical multidimensional scaling
mahal Mahalanobis distance
mdscale Nonclassical multidimensional scaling
pdist Pairwise distance between pairs of objects
squareform Format distance matrix

Cluster Analysis

Hierarchical Clustering

cluster Construct agglomerative clusters from linkages
clusterdata Agglomerative clusters from data
cophenet Cophenetic correlation coefficient
inconsistent Inconsistency coefficient
linkage Agglomerative hierarchical cluster tree
pdist Pairwise distance between pairs of objects
sequentialfs Sequential feature selection
squareform Format distance matrix

k-Means Clustering

kmeans k-means clustering
mahal Mahalanobis distance

Cluster Plots

dendrogram Dendrogram plot
optimalleaforder Optimal leaf ordering for hierarchical clustering
manovacluster Dendrogram of group mean clusters following MANOVA
silhouette Silhouette plot

Gaussian Mixture Models

fitgmdist Fit Gaussian mixture distribution to data
cluster Construct clusters from Gaussian mixture distribution
posterior Posterior probabilities of components
gmdistribution Gaussian mixture models

Procrustes Analysis

procrustes Procrustes analysis

Multivariate Visualization

Multivariate Plots

andrewsplot Andrews plot
biplot Biplot
glyphplot Glyph plot
parallelcoords Parallel coordinates plot

Scatter Plots

gline Interactively add line to plot
gname Add case names to plot
gplotmatrix Matrix of scatter plots by group
gscatter Scatter plot by group
lsline Add least-squares line to scatter plot
refcurve Add reference curve to plot
refline Add reference line to plot
scatterhist Scatter plot with marginal histograms

Industrial Statistics

Design of Experiments (DOE)

Full Factorial Designs

ff2n Two-level full factorial design
fullfact Full factorial design

Fractional Factorial Designs

fracfact Fractional factorial design
fracfactgen Fractional factorial design generators

Response Surface Designs

bbdesign Box-Behnken design
ccdesign Central composite design

D-Optimal Designs

candexch D-optimal design from candidate set using row exchanges
candgen Candidate set generation
cordexch Coordinate exchange
daugment D-optimal augmentation
dcovary D-optimal design with fixed covariates
rowexch Row exchange
rsmdemo Interactive response surface demonstration

Latin Hypercube Designs

lhsdesign Latin hypercube sample
lhsnorm Latin hypercube sample from normal distribution

Quasi-Random Designs

haltonset Halton quasi-random point sets
qrandstream Quasi-random number streams
sobolset Sobol quasi-random point sets

DOE Plots

interactionplot Interaction plot for grouped data
maineffectsplot Main effects plot for grouped data
multivarichart Multivari chart for grouped data
rsmdemo Interactive response surface demonstration
rstool Interactive response surface modeling

Analysis of Lifetime Data

coxphfit Cox proportional hazards regression
ecdf Empirical cumulative distribution function
ecdfhist Histogram based on empirical cumulative distribution function
ksdensity Kernel smoothing function estimate
mle Maximum likelihood estimates
mlecov Asymptotic covariance of maximum likelihood estimators
fitdist Fit probability distribution object to data
dfittool Open Distribution Fitting app
linhyptest Linear hypothesis test
evfit Extreme value parameter estimates
expfit Exponential parameter estimates
gamfit Gamma parameter estimates
lognfit Lognormal parameter estimates
normfit Normal parameter estimates
probplot Probability plots
wblfit Weibull parameter estimates
wblplot Weibull probability plot

Statistical Process Control

capability Process capability indices
capaplot Process capability plot
controlchart Shewhart control charts
controlrules Western Electric and Nelson control rules
gagerr Gage repeatability and reproducibility study
histfit Histogram with a distribution fit
normspec Normal density plot between specifications
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