statistics

statistics

1.9.1 2026-08-27

The Statistics package for GNU Octave.

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Descriptive Statistics

cdfcalc Calculate an empirical cumulative distribution function.
cl_multinom Confidence level of multinomial portions.
dcov Distance correlation, covariance and correlation statistics.
ecdf Empirical (Kaplan-Meier) cumulative distribution function.
geomean Compute the geometric mean of X.
grpstats Summary statistics by group.
harmmean Compute the harmonic mean of X.
jackknife Compute jackknife estimates of a parameter taking one or more given samples as parameters.
ksdensity Kernel smoothing density estimate.
mvksdensity Multivariate kernel smoothing density estimate.
nancov Compute the covariance matrix while ignoring NaN values.
nanmax Find the maximum while ignoring NaN values.
nanmean Compute the mean while ignoring NaN values.
nanmedian Compute the median while ignoring NaN values.
nanmin Find the minimum while ignoring NaN values.
nanstd Compute the standard deviation while ignoring NaN values.
nansum Compute the sum while ignoring NaN values.
nanvar Compute the variance while ignoring NaN values.
partialcorr Linear or rank partial correlation coefficients.
partialcorri Partial correlation of each response with each predictor, adjusting for the remaining predictors.
tabulate Create a frequency table of unique values in vector X.
trimmean Compute the trimmed mean.

Data Manipulation

combnk Return all combinations of K elements in DATA.
crosstab Create a cross-tabulation (contingency table) T from data vectors.
datasample Randomly sample data.
dummyvar Create dummy variables.
fillmissing Fill missing data in arrays.
grp2idx Get index for grouping variable.
ismissing Find missing data in arrays.
isoutlier Find outliers in data
multiway Solve the multiway number partitioning problem.
normalise_distribution Transform a set of data so as to be N(0,1) distributed according to an idea by van Albada and Robinson.
randsample Sample elements from a vector.
rmmissing Remove missing data from arrays.
standardizeMissing Replace selected values by standard missing values.
tiedrank X may be a vector or an array.

Hypothesis Testing

adtest Anderson-Darling goodness-of-fit hypothesis test.
anova Object-oriented interface for analysis of variance.
anova1 Perform a one-way analysis of variance (ANOVA) for comparing the means of two or more groups of data under the null hypothesis that the groups are drawn from distributions with the same mean.
anova2 Performs two-way factorial (crossed) or a nested analysis of variance (ANOVA) for balanced designs.
anovan Perform a multi (N)-way analysis of (co)variance (ANOVA or ANCOVA) to evaluate the effect of one or more categorical or continuous predictors (i.e. independent variables) on a continuous outcome (i.e. dependent variable).
ansaribradley Ansari-Bradley two-sample test for equal dispersions.
bartlett_test Perform a Bartlett test for the homogeneity of variances.
barttest Bartlett's test of sphericity for correlation.
binotest Test for probability P of a binomial sample
chi2gof Chi-square goodness-of-fit test.
chi2test Perform a chi-squared test (for independence or homogeneity).
correlation_test Perform a correlation coefficient test to determine whether two samples X and Y come from uncorrelated populations.
dwtest Durbin-Watson test for autocorrelation in linear regression residuals.
fishertest Fisher's exact test.
friedman Performs the nonparametric Friedman's test to compare column effects in a two-way layout. friedman tests the null hypothesis that the column effects are all the same against the alternative that they are not all the same.
hotelling_t2test Compute Hotelling's T^2 ("T-squared") test for a single sample or two dependent samples (paired-samples).
hotelling_t2test2 Compute Hotelling's T^2 ("T-squared") test for two independent samples.
jbtest Jarque-Bera hypothesis test of composite normality.
kruskalwallis Perform a Kruskal-Wallis test, the non-parametric alternative of a one-way analysis of variance (ANOVA), for comparing the means of two or more groups of data under the null hypothesis that the groups are drawn from the same population, ...
kstest Single sample Kolmogorov-Smirnov (K-S) goodness-of-fit hypothesis test.
kstest2 Two-sample Kolmogorov-Smirnov goodness-of-fit hypothesis test.
levene_test Perform a Levene's test for the homogeneity of variances.
lillietest Lilliefors goodness-of-fit hypothesis test.
manova1 One-way multivariate analysis of variance (MANOVA).
mcnemar_test Perform a McNemar's test on paired nominal data.
multcompare Perform posthoc multiple comparison tests or p-value adjustments to control the family-wise error rate (FWER) or false discovery rate (FDR).
ranksum Wilcoxon rank sum test for equal medians.
regression_ftest F-test for General Linear Regression Analysis
regression_ttest Perform a linear regression t-test.
runstest Run test for randomness in the vector X.
sampsizepwr Sample size and power calculation for hypothesis test.
signrank Wilcoxon signed rank test for median.
signtest Signed test for median.
ttest Test for mean of a normal sample with unknown variance.
ttest2 Perform a t-test to compare the means of two groups of data under the null hypothesis that the groups are drawn from distributions with the same mean.
vartest One-sample test of variance.
vartest2 Two-sample F test for equal variances.
vartestn Test for equal variances across multiple groups.
ztest One-sample Z-test.
ztest2 Two proportions Z-test.

Experimental Design

ff2n Two-level full factorial design.
fullfact Full factorial design.
parseWilkinsonFormula Parse and expand statistical model formulae using the Wilkinson notation.
sigma_pts Calculates 2*N+1 sigma points in N dimensions.
x2fx Convert predictors to design matrix.

Regression

CompactLinearModel Compact linear regression model
CoxModel Cox proportional hazards regression model class.
coxphfit Fit a Cox proportional hazards regression model.
fitcox Fit a Cox proportional hazards regression model.
fitglm Fit a generalized linear regression model.
fitglme Fit a generalized linear mixed-effects model specified by a formula.
fitlm Fit a linear regression model to data and return a ‘LinearModel’ object.
fitlme Fit a linear mixed-effects model specified by a formula.
fitlmematrix Fit a linear mixed-effects model from design matrices.
fitnlm Fit a nonlinear regression model.
GeneralizedLinearMixedModel Generalized linear mixed-effects model fitted to data.
GeneralizedLinearModel Generalized linear regression model class.
glmfit Perform generalized linear model fitting.
glmval Predict values for a generalized linear model.
invpred Inverse prediction from a simple linear regression.
lasso Lasso and elastic-net regularized least-squares regression.
lassoglm Lasso and elastic-net regularized generalized linear model regression.
LinearFormula Model formula of a linear or generalized linear regression.
LinearMixedModel Linear mixed-effects model fitted to data.
LinearModel Linear regression model
logistic_regression Perform ordinal logistic regression.
mnrfit Fit a multinomial logistic regression model.
mnrval Predict values for a multinomial logistic regression model.
monotone_smooth Produce a smooth monotone increasing approximation to a sampled functional dependence.
mvregress Multivariate (multiple-response) linear regression by maximum likelihood.
mvregresslike Negative log-likelihood for a multivariate regression model.
nlinfit Fit a nonlinear regression model.
nlparci Confidence intervals for the coefficients of a nonlinear regression.
nlpredci Confidence intervals for predictions of a nonlinear regression.
NonLinearModel Nonlinear regression model class.
plsregress Calculate partial least squares regression using SIMPLS algorithm.
regress Multiple Linear Regression using Least Squares Fit of Y on X with the model ‘y = X * beta + e’.
regress_gp Regression using Gaussian Processes.
ridge Ridge regression.
robustfit Robust linear regression.
stepwisefit Perform stepwise linear regression using conditional p-value criteria.
stepwiseglm Fit a generalized linear regression model by stepwise term selection.
stepwiselm Fit a linear regression model using stepwise regression and return a ‘LinearModel’ object.

Supervised Learning

ClassificationDiscriminant Discriminant analysis classification
ClassificationGAM Generalized additive model classification
ClassificationKernel Gaussian kernel binary classifier for large data.
ClassificationKNN K-nearest neighbors classification
ClassificationLinear Linear binary classifier for high dimensional data.
ClassificationNaiveBayes Naive Bayes classification
ClassificationNeuralNetwork Neural network classification
ClassificationPartitionedKernel Cross-validated Gaussian kernel binary classifier.
ClassificationPartitionedLinear Cross-validated linear binary classifier.
ClassificationPartitionedModel Cross-validated classification model
ClassificationSVM Support Vector Machine classification
CompactClassificationDiscriminant Compact discriminant analysis classification
CompactClassificationGAM Compact generalized additive model classification
CompactClassificationNaiveBayes Compact naive Bayes classification
CompactClassificationNeuralNetwork Compact neural network classification
CompactClassificationSVM Compact Support Vector Machine classification
CompactRegressionGAM Compact generalized additive model regression
CompactRegressionGP Create a CompactRegressionGP object containing a Gaussian process regression model without its training data.
CompactRegressionNeuralNetwork Create a CompactRegressionNeuralNetwork object, a neural network regression model that has dropped its training data.
CompactRegressionSVM Create a CompactRegressionSVM object, a support vector regression model that has dropped its training data.
fcnnpredict Make predictions from a fully connected Neural Network.
fcnntrain Train a fully connected Neural Network.
fitcdiscr Fit a Linear Discriminant Analysis classification model.
fitcgam Fit a Generalized Additive Model (GAM) for binary classification.
fitckernel Fit a Gaussian kernel binary classifier.
fitcknn Fit a k-Nearest Neighbor classification model.
fitclinear Fit a linear binary classifier.
fitcnb Fit a naive Bayes classification model.
fitcnet Fit a Neural Network classification model.
fitcsvm Fit a Support Vector Machine classification model.
fitrgam Fit a Generalized Additive Model (GAM) for regression.
fitrgp Fit a Gaussian process regression model.
fitrkernel Fit a Gaussian kernel regression model.
fitrlinear Fit a linear regression model.
fitrnet Fit a neural network regression model.
fitrsvm Fit a support vector machine regression model.
gamboostinter Boost trees over selected pairs of predictors.
gamboostpairs Score every pair of predictors for an interaction.
gamboostpredict Predict from a generalized additive model of boosted trees.
gamboosttrain Fit a generalized additive model of boosted trees.
gampredict Evaluate a generalized additive model on new data.
gamtrain Fit a generalized additive model of smoothing splines.
RegressionGAM Create a RegressionGAM class object containing a Generalized Additive Model (GAM) for regression.
RegressionGP Create a RegressionGP object containing a Gaussian process regression model.
RegressionKernel Gaussian kernel regression model for large data.
RegressionLinear Linear regression model for high dimensional data.
RegressionNeuralNetwork Create a RegressionNeuralNetwork object containing a neural network regression model.
RegressionPartitionedKernel Cross-validated Gaussian kernel regression model.
RegressionPartitionedLinear Cross-validated linear regression model.
RegressionPartitionedModel Create a RegressionPartitionedModel object, a regression model cross validated over a partition of its training data.
RegressionSVM Create a RegressionSVM object containing a support vector machine regression model.
svmpredict This function predicts new labels from a testing instance matrix based on an SVM MODEL created with ‘svmtrain’.
svmtrain This function trains an SVM MODEL based on known LABELS and their corresponding DATA which comprise an instance matrix.

Clustering

CalinskiHarabaszEvaluation Calinski-Harabasz clustering evaluation.
cluster Define clusters from an agglomerative hierarchical cluster tree.
ClusterCriterion A clustering evaluation object.
clusterdata Wrapper function for ‘linkage’ and ‘cluster’. If
cophenet Compute the cophenetic correlation coefficient.
DaviesBouldinEvaluation Davies-Bouldin object to evaluate clustering solutions
dbscan Density-Based Spatial Clustering of Applications with Noise (DBSCAN).
evalclusters Create a clustering evaluation object to find the optimal number of clusters.
fitgmdist Fit a Gaussian mixture model with K components to DATA.
GapEvaluation Gap evaluation for clustering solutions
gmdistribution Create an object of the gmdistribution class which represents a Gaussian mixture model with k components of n-dimensional Gaussians.
inconsistent Compute the inconsistency coefficient for each link of a hierarchical cluster tree.
kmeans Perform a K-means clustering of the N*D matrix DATA.
kmedoids Partition observations into K clusters using the k-medoids algorithm.
linkage Produce a hierarchical clustering dendrogram.
optimalleaforder Compute the optimal leaf ordering of a hierarchical binary cluster tree.
SilhouetteEvaluation Silhouette evaluation for clustering
spectralcluster Partition observations into K clusters using spectral clustering.

Nearest Neighbors

createns Create a nearest neighbor searcher object.
editDistance Compute the edit (Levenshtein) distance between strings or documents.
ExhaustiveSearcher Exhaustive nearest neighbor searcher
hnswSearcher Hierarchical Navigable Small World (HNSW) nearest neighbor searcher class.
KDTreeSearcher KD-tree nearest neighbor searcher
knnsearch Find k-nearest neighbors from input data.
mahal Mahalanobis' D-square distance.
pdist Return the distance between any two rows in X.
pdist2 Compute pairwise distance between two sets of vectors.
rangesearch Find all neighbors within specified distance from input data.
squareform Interchange between distance matrix and distance vector formats.

Anomaly Detection

iforest Detect anomalies with an isolation forest.
IsolationForest Isolation Forest model for anomaly detection.
LocalOutlierFactor Local Outlier Factor model for anomaly detection.
lof Detect anomalies with the Local Outlier Factor (LOF) method.
ocsvm Detect anomalies with a one-class support vector machine.
OneClassSVM One-class support vector machine model for anomaly detection.
robustcov Robust multivariate covariance and mean estimate.

Dimensionality Reduction

canoncorr Canonical correlation analysis.
cmdscale Classical multidimensional scaling of a matrix.
factoran Common factor analysis.
mdscale Nonclassical (metric and nonmetric) multidimensional scaling.
nnmf Nonnegative matrix factorization.
pca Performs a principal component analysis on a data matrix.
pcacov Perform principal component analysis on covariance matrix
pcares Calculate residuals from principal component analysis.
ppca Probabilistic principal component analysis.
princomp Performs a principal component analysis on a NxP data matrix X.
procrustes Procrustes Analysis.
ReconstructionICA Reconstruction independent component analysis (RICA) feature-extraction model.
rica Reconstruction independent component analysis (RICA) for feature extraction.
rotatefactors Rotate a factor-loading matrix.
sparsefilt Sparse filtering for feature extraction.
SparseFiltering Sparse filtering feature-extraction model.
tsne t-distributed stochastic neighbor embedding (t-SNE).

Model Evaluation

confusionchart Display a chart of a confusion matrix.
confusionmat Compute a confusion matrix for classification problems
ConfusionMatrixChart Confusion matrix chart for classification results
crossval Perform cross validation on given data.
cvpartition Partition data for cross-validation
perfcurve Receiver operating characteristic (ROC) and other classifier performance curves.
rocmetrics Receiver operating characteristic (ROC) metrics for classifier output.

Markov Models

hmmdecode Posterior state probabilities of a hidden Markov model.
hmmestimate Estimation of a hidden Markov model for a given sequence.
hmmgenerate Output sequence and hidden states of a hidden Markov model.
hmmtrain Estimate the parameters of a hidden Markov model from emitted sequences.
hmmviterbi Viterbi path of a hidden Markov model.

Random Sampling

johnsrnd Random arrays from the Johnson system of distributions.
mhsample Draws NSAMPLES samples from a target stationary distribution PDF using Metropolis-Hastings algorithm.
pearsrnd Random arrays from the Pearson system of distributions.
qrandn Returns random deviates drawn from a q-Gaussian distribution.
slicesample Draws NSAMPLES samples from a target stationary distribution PDF using slice sampling of Radford M.

Distribution Classes

paretotails Piecewise distribution with generalized Pareto tails.
prob.ProbabilityDistribution Abstract base class of the probability distribution objects.
prob.BetaDistribution Beta probability distribution object.
prob.BinomialDistribution Binomial probability distribution object.
prob.BirnbaumSaundersDistribution Birnbaum-Saunders probability distribution object.
prob.BurrDistribution Burr probability distribution object.
prob.ExponentialDistribution Exponential probability distribution object.
prob.ExtremeValueDistribution Extreme value probability distribution object.
prob.GammaDistribution Gamma probability distribution object.
prob.GeneralizedExtremeValueDistribution Generalized extreme value probability distribution object.
prob.GeneralizedParetoDistribution Generalized Pareto probability distribution object.
prob.HalfNormalDistribution Half-normal probability distribution object.
prob.InverseGaussianDistribution Inverse Gaussian probability distribution object.
prob.KernelDistribution Kernel probability distribution object.
prob.LogisticDistribution Logistic probability distribution object.
prob.LoglogisticDistribution Log-logistic probability distribution object.
prob.LognormalDistribution Lognormal probability distribution object.
prob.LoguniformDistribution Log-uniform probability distribution object.
prob.MultinomialDistribution Multinomial probability distribution object.
prob.NakagamiDistribution Nakagami probability distribution object.
prob.NegativeBinomialDistribution Negative binomial probability distribution object.
prob.NormalDistribution Normal probability distribution object.
prob.PiecewiseLinearDistribution Piecewise linear probability distribution object.
prob.PoissonDistribution Poisson probability distribution object.
prob.RayleighDistribution Rayleigh probability distribution object.
prob.RicianDistribution Rician probability distribution object.
prob.StableDistribution Stable probability distribution object.
prob.tLocationScaleDistribution Location-Scale Student's T probability distribution object.
prob.TriangularDistribution Triangular probability distribution object.
prob.UniformDistribution Continuous uniform probability distribution object.
prob.WeibullDistribution Weibull probability distribution object.

Distribution Fitting

betafit Estimate parameters and confidence intervals for the Beta distribution.
betalike Negative log-likelihood for the Beta distribution.
binofit Estimate parameter and confidence intervals for the binomial distribution.
binolike Negative log-likelihood for the binomial distribution.
bisafit Estimate mean and confidence intervals for the Birnbaum-Saunders distribution.
bisalike Negative log-likelihood for the Birnbaum-Saunders distribution.
burrfit Estimate mean and confidence intervals for the Burr type XII distribution.
burrlike Negative log-likelihood for the Burr type XII distribution.
copulafit Fit a copula to data.
evfit Estimate parameters and confidence intervals for the extreme value distribution.
evlike Negative log-likelihood for the extreme value distribution.
expfit Estimate mean and confidence intervals for the exponential distribution.
explike Negative log-likelihood for the exponential distribution.
gamfit Estimate parameters and confidence intervals for the Gamma distribution.
gamlike Negative log-likelihood for the Gamma distribution.
geofit Estimate parameter and confidence intervals for the geometric distribution.
gevfit Estimate parameters and confidence intervals for the generalized extreme value (GEV) distribution.
gevlike Negative log-likelihood for the generalized extreme value (GEV) distribution.
gevfit_lmom Find an estimator (PARAMHAT) of the generalized extreme value (GEV) distribution fitting DATA using the method of L-moments.
gpfit Estimate parameters and confidence intervals for the generalized Pareto distribution.
gplike Negative log-likelihood for the generalized Pareto distribution.
gumbelfit Estimate parameters and confidence intervals for Gumbel distribution.
gumbellike Negative log-likelihood for the extreme value distribution.
hnfit Estimate parameters and confidence intervals for the half-normal distribution.
hnlike Negative log-likelihood for the half-normal distribution.
invgfit Estimate mean and confidence intervals for the inverse Gaussian distribution.
invglike Negative log-likelihood for the inverse Gaussian distribution.
logifit Estimate mean and confidence intervals for the logistic distribution.
logilike Negative log-likelihood for the logistic distribution.
loglfit Estimate mean and confidence intervals for the log-logistic distribution.
logllike Negative log-likelihood for the log-logistic distribution.
lognfit Estimate parameters and confidence intervals for the lognormal distribution.
lognlike Negative log-likelihood for the lognormal distribution.
nakafit Estimate mean and confidence intervals for the Nakagami distribution.
nakalike Negative log-likelihood for the Nakagami distribution.
nbinfit Estimate parameter and confidence intervals for the negative binomial distribution.
nbinlike Negative log-likelihood for the negative binomial distribution.
normfit Estimate parameters and confidence intervals for the normal distribution.
normlike Negative log-likelihood for the normal distribution.
poissfit Estimate parameter and confidence intervals for the Poisson distribution.
poisslike Negative log-likelihood for the Poisson distribution.
raylfit Estimate parameter and confidence intervals for the Rayleigh distribution.
rayllike Negative log-likelihood for the Rayleigh distribution.
ricefit Estimate parameters and confidence intervals for the Rician distribution.
ricelike Negative log-likelihood for the Rician distribution.
stblfit Estimate parameters and confidence intervals for the stable distribution.
stbllike Negative log-likelihood for the stable distribution.
tlsfit Estimate parameters and confidence intervals for the Location-scale Student's T distribution.
tlslike Negative log-likelihood for the location-scale Student's T distribution.
unidfit Estimate parameter and confidence intervals for the discrete uniform distribution.
unifit Estimate parameters and confidence intervals for the continuous uniform distribution.
wblfit Estimate parameters and confidence intervals for the Weibull distribution.
wbllike Negative log-likelihood for the Weibull distribution.

Distribution Functions

betacdf Beta cumulative distribution function (CDF).
betainv Inverse of the Beta distribution (iCDF).
betapdf Beta probability density function (PDF).
betarnd Random arrays from the Beta distribution.
binocdf Binomial cumulative distribution function (CDF).
binoinv Inverse of the Binomial cumulative distribution function (iCDF).
binopdf Binomial probability density function (PDF).
binornd Random arrays from the Binomial distribution.
bisacdf Birnbaum-Saunders cumulative distribution function (CDF).
bisainv Inverse of the Birnbaum-Saunders cumulative distribution function (iCDF).
bisapdf Birnbaum-Saunders probability density function (PDF).
bisarnd Random arrays from the Birnbaum-Saunders distribution.
burrcdf Burr type XII cumulative distribution function (CDF).
burrinv Inverse of the Burr type XII cumulative distribution function (iCDF).
burrpdf Burr type XII probability density function (PDF).
burrrnd Random arrays from the Burr type XII distribution.
bvncdf Bivariate normal cumulative distribution function (CDF).
bvtcdf Bivariate Student's t cumulative distribution function (CDF).
cauchycdf Cauchy cumulative distribution function (CDF).
cauchyinv Inverse of the Cauchy cumulative distribution function (iCDF).
cauchypdf Cauchy probability density function (PDF).
cauchyrnd Random arrays from the Cauchy distribution.
chi2cdf Chi-squared cumulative distribution function (CDF).
chi2inv Inverse of the chi-squared cumulative distribution function (iCDF).
chi2pdf Chi-squared probability density function (PDF).
chi2rnd Random arrays from the chi-squared distribution.
copulacdf Copula family cumulative distribution functions (CDF).
copulapdf Copula family probability density functions (PDF).
copularnd Random arrays from the copula family distributions.
evcdf Extreme value cumulative distribution function (CDF).
evinv Inverse of the extreme value cumulative distribution function (iCDF).
evpdf Extreme value probability density function (PDF).
evrnd Random arrays from the extreme value distribution.
expcdf Exponential cumulative distribution function (CDF).
expinv Inverse of the exponential cumulative distribution function (iCDF).
exppdf Exponential probability density function (PDF).
exprnd Random arrays from the exponential distribution.
fcdf F-cumulative distribution function (CDF).
finv Inverse of the F-cumulative distribution function (iCDF).
fpdf F-probability density function (PDF).
frnd Random arrays from the F-distribution.
gamcdf Gamma cumulative distribution function (CDF).
gaminv Inverse of the Gamma cumulative distribution function (iCDF).
gampdf Gamma probability density function (PDF).
gamrnd Random arrays from the Gamma distribution.
geocdf Geometric cumulative distribution function (CDF).
geoinv Inverse of the geometric cumulative distribution function (iCDF).
geopdf Geometric probability density function (PDF).
geornd Random arrays from the geometric distribution.
gevcdf Generalized extreme value (GEV) cumulative distribution function (CDF).
gevinv Inverse of the generalized extreme value (GEV) cumulative distribution function (iCDF).
gevpdf Generalized extreme value (GEV) probability density function (PDF).
gevrnd Random arrays from the generalized extreme value (GEV) distribution.
gpcdf Generalized Pareto cumulative distribution function (CDF).
gpinv Inverse of the generalized Pareto cumulative distribution function (iCDF).
gppdf Generalized Pareto probability density function (PDF).
gprnd Random arrays from the generalized Pareto distribution.
gumbelcdf Gumbel cumulative distribution function (CDF).
gumbelinv Inverse of the Gumbel cumulative distribution function (iCDF).
gumbelpdf Gumbel probability density function (PDF).
gumbelrnd Random arrays from the Gumbel distribution.
hncdf Half-normal cumulative distribution function (CDF).
hninv Inverse of the half-normal cumulative distribution function (iCDF).
hnpdf Half-normal probability density function (PDF).
hnrnd Random arrays from the half-normal distribution.
hygecdf Hypergeometric cumulative distribution function (CDF).
hygeinv Inverse of the hypergeometric cumulative distribution function (iCDF).
hygepdf Hypergeometric probability density function (PDF).
hygernd Random arrays from the hypergeometric distribution.
invgcdf Inverse Gaussian cumulative distribution function (CDF).
invginv Inverse of the inverse Gaussian cumulative distribution function (iCDF).
invgpdf Inverse Gaussian probability density function (PDF).
invgrnd Random arrays from the inverse Gaussian distribution.
iwishpdf Compute the probability density function of the inverse Wishart distribution.
iwishrnd Return a random matrix sampled from the inverse Wishart distribution with given parameters.
jsucdf Johnson SU cumulative distribution function (CDF).
jsupdf Johnson SU probability density function (PDF).
laplacecdf Laplace cumulative distribution function (CDF).
laplaceinv Inverse of the Laplace cumulative distribution function (iCDF).
laplacepdf Laplace probability density function (PDF).
laplacernd Random arrays from the Laplace distribution.
logicdf Logistic cumulative distribution function (CDF).
logiinv Inverse of the logistic cumulative distribution function (iCDF).
logipdf Logistic probability density function (PDF).
logirnd Random arrays from the logistic distribution.
loglcdf Loglogistic cumulative distribution function (CDF).
loglinv Inverse of the log-logistic cumulative distribution function (iCDF).
loglpdf Loglogistic probability density function (PDF).
loglrnd Random arrays from the loglogistic distribution.
logncdf Lognormal cumulative distribution function (CDF).
logninv Inverse of the lognormal cumulative distribution function (iCDF).
lognpdf Lognormal probability density function (PDF).
lognrnd Random arrays from the lognormal distribution.
mnpdf Multinomial probability density function (PDF).
mnrnd Random arrays from the multinomial distribution.
mvncdf Multivariate normal cumulative distribution function (CDF).
mvnpdf Multivariate normal probability density function (PDF).
mvnrnd Random vectors from the multivariate normal distribution.
mvtcdf Multivariate Student's t cumulative distribution function (CDF).
mvtpdf Multivariate Student's t probability density function (PDF).
mvtrnd Random vectors from the multivariate Student's t distribution.
nakacdf Nakagami cumulative distribution function (CDF).
nakainv Inverse of the Nakagami cumulative distribution function (iCDF).
nakapdf Nakagami probability density function (PDF).
nakarnd Random arrays from the Nakagami distribution.
nbincdf Negative binomial cumulative distribution function (CDF).
nbininv Inverse of the negative binomial cumulative distribution function (iCDF).
nbinpdf Negative binomial probability density function (PDF).
nbinrnd Random arrays from the negative binomial distribution.
ncfcdf Noncentral F-cumulative distribution function (CDF).
ncfinv Inverse of the noncentral F-cumulative distribution function (iCDF).
ncfpdf Noncentral F-probability density function (PDF).
ncfrnd Random arrays from the noncentral F-distribution.
nctcdf Noncentral t-cumulative distribution function (CDF).
nctinv Inverse of the non-central t-cumulative distribution function (iCDF).
nctpdf Noncentral t-probability density function (PDF).
nctrnd Random arrays from the noncentral t-distribution.
ncx2cdf Noncentral chi-squared cumulative distribution function (CDF).
ncx2inv Inverse of the noncentral chi-squared cumulative distribution function (iCDF).
ncx2pdf Noncentral chi-squared probability distribution function (PDF).
ncx2rnd Random arrays from the noncentral chi-squared distribution.
normcdf Normal cumulative distribution function (CDF).
norminv Inverse of the normal cumulative distribution function (iCDF).
normpdf Normal probability density function (PDF).
normrnd Random arrays from the normal distribution.
plcdf Piecewise linear cumulative distribution function (CDF).
plinv Inverse of the piecewise linear distribution (iCDF).
plpdf Piecewise linear probability density function (PDF).
plrnd Random arrays from the piecewise linear distribution.
poisscdf Poisson cumulative distribution function (CDF).
poissinv Inverse of the Poisson cumulative distribution function (iCDF).
poisspdf Poisson probability density function (PDF).
poissrnd Random arrays from the Poisson distribution.
raylcdf Rayleigh cumulative distribution function (CDF).
raylinv Inverse of the Rayleigh cumulative distribution function (iCDF).
raylpdf Rayleigh probability density function (PDF).
raylrnd Random arrays from the Rayleigh distribution.
ricecdf Rician cumulative distribution function (CDF).
riceinv Inverse of the Rician distribution (iCDF).
ricepdf Rician probability density function (PDF).
ricernd Random arrays from the Rician distribution.
stblcdf Stable cumulative distribution function (CDF).
stblinv Inverse of the stable cumulative distribution function (iCDF).
stblpdf Stable probability density function (PDF).
stblrnd Random arrays from the stable distribution.
tcdf Student's T cumulative distribution function (CDF).
tinv Inverse of the Student's T cumulative distribution function (iCDF).
tpdf Student's T probability density function (PDF).
trnd Random arrays from the Student's T distribution.
tlscdf Location-scale Student's T cumulative distribution function (CDF).
tlsinv Inverse of the location-scale Student's T cumulative distribution function (iCDF).
tlspdf Location-scale Student's T probability density function (PDF).
tlsrnd Random arrays from the location-scale Student's T distribution.
tricdf Triangular cumulative distribution function (CDF).
triinv Inverse of the triangular cumulative distribution function (iCDF).
tripdf Triangular probability density function (PDF).
trirnd Random arrays from the triangular distribution.
unidcdf Discrete uniform cumulative distribution function (CDF).
unidinv Inverse of the discrete uniform cumulative distribution function (iCDF).
unidpdf Discrete uniform probability density function (PDF).
unidrnd Random arrays from the discrete uniform distribution.
unifcdf Continuous uniform cumulative distribution function (CDF).
unifinv Inverse of the continuous uniform cumulative distribution function (iCDF).
unifpdf Continuous uniform probability density function (PDF).
unifrnd Random arrays from the continuous uniform distribution.
vmcdf Von Mises probability density function (PDF).
vminv Inverse of the von Mises cumulative distribution function (iCDF).
vmpdf Von Mises probability density function (PDF).
vmrnd Random arrays from the von Mises distribution.
wblcdf Weibull cumulative distribution function (CDF).
wblinv Inverse of the Weibull cumulative distribution function (iCDF).
wblpdf Weibull probability density function (PDF).
wblrnd Random arrays from the Weibull distribution.
wienrnd Return a simulated realization of the D-dimensional Wiener Process on the interval [0, T].
wishpdf Compute the probability density function of the Wishart distribution
wishrnd Return a random matrix sampled from the Wishart distribution with given parameters

Distribution Statistics

betastat Compute statistics of the Beta distribution.
binostat Compute statistics of the binomial distribution.
bisastat Compute statistics of the Birnbaum-Saunders distribution.
burrstat Compute statistics of the Burr type XII distribution.
chi2stat Compute statistics of the chi-squared distribution.
copulaparam Copula parameter as a function of rank correlation.
copulastat Rank correlation for a copula family.
evstat Compute statistics of the extreme value distribution.
expstat Compute statistics of the exponential distribution.
fstat Compute statistics of the F-distribution.
gamstat Compute statistics of the Gamma distribution.
geostat Compute statistics of the geometric distribution.
gevstat Compute statistics of the generalized extreme value distribution.
gpstat Compute statistics of the generalized Pareto distribution.
hnstat Compute statistics of the half-normal distribution.
hygestat Compute statistics of the hypergeometric distribution.
invgstat Compute statistics of the inverse Gaussian distribution.
logistat Compute statistics of the logistic distribution.
loglstat Compute statistics of the loglogistic distribution.
lognstat Compute statistics of the lognormal distribution.
nakastat Compute statistics of the Nakagami distribution.
nbinstat Compute statistics of the negative binomial distribution.
ncfstat Compute statistics for the noncentral F-distribution.
nctstat Compute statistics for the noncentral t-distribution.
ncx2stat Compute statistics for the noncentral chi-squared distribution.
normstat Compute statistics of the normal distribution.
plstat Compute statistics of the piecewise linear distribution.
poisstat Compute statistics of the Poisson distribution.
raylstat Compute statistics of the Rayleigh distribution.
ricestat Compute statistics of the Rician distribution.
tlsstat Compute statistics of the location-scale Student's T distribution.
tristat Compute statistics of the Triangular distribution.
tstat Compute statistics of the Student's T distribution.
unidstat Compute statistics of the discrete uniform cumulative distribution.
unifstat Compute statistics of the continuous uniform cumulative distribution.
wblstat Compute statistics of the Weibull distribution.

Distribution Wrappers

cdf Return the CDF of a univariate distribution evaluated at X.
fitdist Create probability distribution object.
icdf Return the inverse CDF of a univariate distribution evaluated at P.
makedist Create probability distribution object.
mle Compute maximum likelihood estimates.
mlecov Asymptotic covariance matrix of maximum likelihood estimators.
pdf Return the PDF of a univariate distribution evaluated at X.
random Random arrays from a given one-, two-, or three-parameter distribution.

Plotting

andrewsplot Create an Andrews plot of the multivariate data in X.
bar3 Plot a 3D bar graph.
bar3h Plot a horizontal 3D bar graph.
biplot Create a biplot of the coefficients in COEFS.
boxplot Produce a box plot.
cdfplot Display an empirical cumulative distribution function.
dendrogram Plot a dendrogram of a hierarchical binary cluster tree.
ecdfhist Create a histogram from the output of ‘ecdf’.
einstein Plots the tiling of the basic clusters of einstein tiles.
glyphplot Create a star (glyph) plot of the multivariate data in X.
gplotmatrix Create a matrix of scatter plots grouped by a categorical variable.
gscatter Draw a scatter plot with grouped data.
hist3 Produce bivariate (2D) histogram counts or plots.
histfit Plot histogram with superimposed distribution fit.
manovacluster Cluster group means using manova1 output.
normplot Produce normal probability plot of the data in X.
parallelcoords Create a parallel coordinates plot of the multivariate data in X.
ppplot Perform a PP-plot (probability plot).
probplot Produce a probability plot of the data in Y against the distribution DIST.
qqplot Perform a QQ-plot (quantile plot).
scatterhist Create a scatter plot of X and Y with marginal histograms.
silhouette Compute the silhouette values of clustered data and show them on a plot.
violin Produce a Violin plot of the data X.
wblplot Plot a column vector DATA on a Weibull probability plot using rank regression.

I/O

libsvmread This function reads the labels and the corresponding instance_matrix from a LIBSVM data file and stores them in LABELS and DATA respectively.
libsvmwrite This function saves the labels and the corresponding instance_matrix in a file specified by FILENAME.
loadmodel Load a Classification or Regression model from a file.

Utilities

cholcov Cholesky-like decomposition for covariance matrix.
logit Compute the logit for each value of P
makima Compute the 1-D Modified Akima piecewise cubic Hermite interpolant of sample data X and Y.
probit Probit transformation
statget Read one option out of a statistics options structure.
statset Create or modify an options structure for iterative statistics algorithms.