Octave

Statistics package

Revision as of 14:12, 21 February 2023 by Pr0m1th3as (talk | contribs) (→‎Clustering)

The statistics package is part of the Octave Packages. Since version 1.5.0, the statistics package requires Octave version 6.1 or higher. From Octave v7.2 or later, you can install the latest statistics package (currently 1.5.3) with the following command:

pkg install -forge statistics

The following sections provide an overview of the functions available in the statistics package sorted alphabetically and arranged in groups similarly to the package's INDEX file. the TODO subsections are only informative of the current development plans for the forthcoming releases and they are not intended for reporting bugs, missing features or incompatibilities. Please report these in the statistics repository at GitHub.

Clustering

Available functions

The following table lists the available functions for clustering data.

Function Description
cluster Define clusters from an agglomerative hierarchical cluster tree.
clusterdata Wrapper function for 'linkage' and 'cluster'.
cmdscale Classical multidimensional scaling of a matrix.
confusionmat Compute a confusion matrix for classification problems.
cophenet Compute the cophenetic correlation coefficient.
evalclusters Create a clustering evaluation object to find the optimal number of clusters.
inconsistent Compute the inconsistency coefficient for each link of a hierarchical cluster tree.
kmeans Perform a K-means clustering of an NxD matrix.
linkage Produce a hierarchical clustering dendrogram.
mahal Mahalanobis' D-square distance.
mhsample Draws NSAMPLES samples from a target stationary distribution PDF using Metropolis-Hastings algorithm.
optimalleaforder Compute the optimal leaf ordering of a hierarchical binary cluster tree.
pdist Return the distance between any two rows in X.
pdist2 Compute pairwise distance between two sets of vectors.
slicesample Draws NSAMPLES samples from a target stationary distribution PDF using slice sampling of Radford M. Neal.
squareform Interchange between distance matrix and distance vector formats.

TODO list

Missing functions:

  • procrustes

Data Manipulation

Available functions

The following table lists the available functions for data manipulation.

Function Description
combnk Return all combinations of K elements in DATA.
crosstab Create a cross-tabulation (contingency table) T from data vectors.
datasample Randomly sample data.
fillmissing Replace missing entries of array A either with values in v or as determined by other specified methods.
grp2idx Get index for group variables.
ismissing Find missing data in a numeric or string array.
normalise_distribution Transform a set of data so as to be N(0,1) distributed according to an idea by van Albada and Robinson.
rmmissing Remove missing or incomplete data from an array.
standardizeMissing Replace data values specified by indicator in A by the standard ’missing’ data value for that data type.
tabulate Compute a frequency table.

Descriptive Statistics

Available functions

The following table lists the available functions for descriptive statistics.

Function Description
geomean Compute the geometric mean.
grpstats Compute summary statistics by group. Fully MATLAB compatible.
harmmean Compute the harmonic mean.
jackknife Compute jackknife estimates of a parameter taking one or more given samples as parameters.
mean Compute the mean. Fully MATLAB compatible.
median Compute the median. Fully MATLAB compatible.
nanmax Find the maximal element while ignoring NaN values.
nanmin Find the minimal element while ignoring NaN values.
nansum Compute the sum while ignoring NaN values.
std Compute the standard deviation. Fully MATLAB compatible.
trimmean Compute the trimmed mean.
std Compute the variance. Fully MATLAB compatible.

In external packages

bootci, bootstrp are implemented in the statistics-bootstrap package.

Shadowing Octave core functions

The following functions will shadow the respective core functions until Octave 9.

  • mean
  • median
  • std
  • var

TODO list

Update trimmean function to be fully MATLAB compatible.

Re-introduce the nan* functions implemented in C++ with the "all" and "vecdim" options.

Re-implement the following functions from core Octave, as shadowing functions with updated functionality regarding the "all", "omitnan", and "vecdim" options, with the intend to be included in Octave 9.

  • cov
  • mad
  • meansq
  • mode
  • moment

Distributions

Available functions

The following table lists the cdf, icdf, pdf, and random functions available in the statistics package. Since version 1.5.3, all CDFs support the "upper" option for evaluating the complement of the respective CDF.

Note! The icdf wrapper for the quantile functions is not implemented yet.

Distribution Name Cumulative Distribution Function Quantile Function Probability Density Function Random Generator
Birnbaum–Saunders bbscdf bbsinv bbspdf bbsrnd
Beta betacdf betainv betapdf betarndbivariate
[Binomial binocdf binoinv binopdf binornd
Bivariate bvncdf
Burr Type XII burrcdf burrinv burrpdf burrrnd
Cauchy cauchy_cdf cauchy_inv cauchy_pdf cauchy_rnd
Chi-squared chi2cdf chi2inv chi2pdf chi2rnd
Copula Family copulacdf copulainv copulapdf copularnd
Extreme Value evcdf evinv evpdf evrnd
Exponential expcdf expinv exppdf exprnd
F fcdf finv fpdf frnd
Gamma gamcdf gaminv gampdf gamrnd
Geometric geocdf geoinv geopdf geornd
Generalized Extreme Value gevcdf gevinv gevpdf gevrnd
Generalized Pareto gpcdf gpinv gppdf gprnd
Hypergeometric hygecdf hygeinv hygepdf hygernd
Inverse-Wishart iwishpdf iwishrnd
Johnson's SU jsucdf jsupdf
Laplace laplace_cdf laplace_inv laplace_pdf laplace_rnd
Logistic logistic_cdf logistic_inv logistic_pdf logistic_rnd
Log-normal logncdf logninv lognpdf lognrnd
Multinomial mnpdf mnrnd
Multivariate Normal mvncdf mvninv mvnpdf mvnrnd
Multivariate Student's T mvtcdf mvtcdfqmc mvtinv mvtpdf mvtrnd
Nakagami nakacdf nakainv nakapdf nakarnd
Negative Binomial nbincdf nbininv nbinpdf nbinrnd
Noncentral F ncfcdf ncfinv ncfpdf ncfrnd
Noncentral Student's T nctcdf nctinv nctpdf nctrnd
Noncentral Chi-squared ncx2cdf ncx2inv ncx2pdf ncx2rnd
Normal normcdf norminv normpdf normrnd
Poisson poisscdf poissinv poisspdf poissrnd
Rayleigh raylcdf raylinv raylpdf raylrnd
Standard Normal stdnormal_cdf stdnormal_inv stdnormal_pdf stdnormal_rnd
Student's T tcdf tinv tpdf trnd
Triangular tricdf triinv tripdf trirnd
Discrete Uniform unidcdf unidinv unidpdf unidrnd
Continuous Uniform unifcdf unifinv unifpdf unifrnd
von Mises vmcdf vmpdf vmrnd
Weibull wblcdf wblinv wblpdf wblrnd
Wiener process wienrnd
Wishart wishpdf wishrnd

Distribution Fitting

Functions available for estimating parameters and the negative log-likelihood for certain distributions.

Distribution Name Parameter Estimation Negativel Log-likelihood
Extreme Value evfit evlike
Exponential expfit explike
Gamma gamfit gamlike
Generalized Extreme Value gevfit_lmom gevfit gevlike
Generalized Pareto gpfit gplike
Normal normlike

Distribution Statistics

Functions available for computing mean and variance from distribution parameters.

  • betastat
  • binostat
  • chi2stat
  • evstat
  • expstat
  • fstat
  • gamstat
  • geostat
  • gevstat
  • gpstat
  • hygestat
  • lognstat
  • nbinstat
  • ncfstat
  • nctstat
  • ncx2stat
  • normstat
  • poisstat
  • raylstat
  • fitgmdist
  • tstat
  • unidstat
  • unifstat
  • wblstat

Experimental Design

Available functions

Functions available for computing design matrices.

Function Description
fullfact Full factorial design.
ff2n Two-level full factorial design.
sigma_pts Calculates 2*N+1 sigma points in N dimensions.
x2fx Convert predictors to design matrix.

Machine Learning

Available functions

The following table lists the available functions.

Function Description
hmmestimate Estimation of a hidden Markov model for a given sequence.
hmmgenerate Output sequence and hidden states of a hidden Markov model.
hmmviterbi Viterbi path of a hidden Markov model.
svmpredict Perform a K-means clustering of an NxD matrix.
svmtrain Produce a hierarchical clustering dendrogram.

TODO list

Update svmpredict and svmtrain to libsvm 3.0.

Missing functions:

  • hmmdecode
  • hmmtrain

Model Fitting

Available functions

Functions available for fitting or evaluating statistical models.

Function Description
crossval Perform cross validation on given data.
fitgmdist Fit a Gaussian mixture model with K components to DATA.
fitlm Regress the continuous outcome (i.e. dependent variable) Y on continuous or categorical predictors (i.e. independent variables) X by minimizing the sum-of-squared residuals.

Cross Validation

Class of set partitions for cross-validation, used in crossval

  • @cvpartition/cvpartition
  • @cvpartition/display
  • @cvpartition/get
  • @cvpartition/repartition
  • @cvpartition/set
  • @cvpartition/test
  • @cvpartition/training

TODO list

Missing functions:

  • anova
  • manova

Hypothesis Testing

Available functions

Functions available for hypothesis testing

Function Description
adtest Anderson-Darling goodness-of-fit hypothesis test.
anova1 Perform a one-way analysis of variance (ANOVA)
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).
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).
friedman Performs the nonparametric Friedman's test to compare column effects in a two-way layout.
https://gnu-octave.github.io/statistics/hotelling_t2test.html 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.
kruskalwallis Perform a Kruskal-Wallis test, the non-parametric alternative of a one-way analysis of variance (ANOVA).
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.
manova1 One-way multivariate analysis of variance (MANOVA).
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. This test is equivalent to a Mann-Whitney U-test.
regression_ftest F-test for General Linear Regression Analysis
regression_ttest Perform a linear regression t-test.
runstest Runs test for detecting serial correlation in the vector X.
sampsizepwr Sample size and power calculation for hypothesis test.
signtest Test for median.
ttest Test for mean of a normal sample with unknown variance or a paired-sample t-test.
ttest2 Perform a two independent samples t-test.
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.

TODO list

Missing functions:

  • fishertest
  • meanEffectSize

Plotting

Available functions

The following table lists the available functions for plotting data.

Function Description
boxplot Produce a box plot.
cdfplot Display an empirical cumulative distribution function.
confusionchart Display a chart of a confusion matrix.
dendrogram Plot a dendrogram of a hierarchical binary cluster tree.
ecdf Empirical (Kaplan-Meier) cumulative distribution function.
gscatter Draw a scatter plot with grouped data.
histfit Plot histogram with superimposed fitted normal density.
hist3 Produce bivariate (2D) histogram counts or plots.
manovacluster Cluster group means using manova1 output.
normplot Produce normal probability plot of the data.
ppplot Perform a PP-plot (probability plot).
qqplot Perform a QQ-plot (quantile plot).
silhouette Compute the silhouette values of clustered data and show them on a plot.
violin Produce a Violin plot of the data.
wblplot Plot a column vector DATA on a Weibull probability plot using rank regression.

TODO list

Missing functions:

  • andrewsplot
  • bar3
  • bar3h
  • glyphplot
  • gplotmatrix
  • parallelcoords

Regression

Available functions

The following table lists the available functions for regression analysis.

Function Description
canoncorr Canonical correlation analysis.
cholcov Cholesky-like decomposition for covariance matrix.
dcov Distance correlation, covariance and correlation statistics.
logistic_regression Perform ordinal logistic regression.
monotone_smooth Produce a smooth monotone increasing approximation to a sampled functional dependence.
pca Performs a principal component analysis on a data matrix.
pcacov Perform principal component analysis on the NxN covariance matrix X
pcares Calculate residuals from principal component analysis.
plsregress Calculate partial least squares regression using SIMPLS algorithm.
princomp Performs a principal component analysis on a NxP data matrix.
regress Multiple Linear Regression using Least Squares Fit.
regress_gp Linear scalar regression using gaussian processes.
stepwisefit Linear regression with stepwise variable selection.

TODO list

Missing functions:

  • glmfit
  • glmval
  • mnrfit
  • mnrval

Wrappers

Available functions

Functions available for wrapping other functions or group of functions.

Function Description
cdf This is a wrapper for the NAMEcdf and NAME_cdf functions available in the statistics package.
icdf This is a wrapper for the NAMEinv and NAME_inv functions available in the statistics package.
pdf This is a wrapper for the NAMEpdf and NAME_pdf functions available in the statistics package.
random Generates pseudo-random numbers from a given one-, two-, or three-parameter distribution.
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