statistics
Additional statistics functions for Octave.
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Distributions
Descriptive statistics
Experimental design
Regression
Plots
Models
Hypothesis testing
Fitting
Clustering
Reading and Writing
Cvpartition (class of set partitions for cross-validation, used in crossval)
Categorical data
Classification Performance Evaluation
Other
Return the CDF for the given Anderson-Darling coefficient A computed from N values sampled from a distribution.
For each element of X, compute the cumulative distribution function (CDF) at X of the Birnbaum-Saunders distribution with parameters LOCATION, SCALE and SHAPE.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Birnbaum-Saunders distribution with parameters LOCATION, SCALE, and SHAPE.
For each element of X, compute the probability density function (PDF) at X of the Birnbaum-Saunders distribution with parameters LOCATION, SCALE and SHAPE.
Return a matrix of random samples from the Birnbaum-Saunders distribution with parameters LOCATION, SCALE and SHAPE.
Compute mean and variance of the beta distribution.
Compute mean and variance of the binomial distribution.
Test for probability P of a binomial sample
For each element of X, compute the cumulative distribution function (CDF) at X of the Burr distribution with scale parameter ALPHA and shape parameters C and K.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Burr distribution with scale parameter ALPHA and shape parameters C and K.
For each element of X, compute the probability density function (PDF) at X of the Burr distribution with scale parameter ALPHA and shape parameters C and K.
Return a matrix of random samples from the generalized Pareto distribution with scale parameter ALPHA and shape parameters C and K.
Return cumulative density function of NAME function for value X.
Compute mean and variance of the chi-square distribution.
Returns confidence level of multinomial parameters estimated p = x / sum(x) with predefined confidence interval B.
Compute the cumulative distribution function of a copula family.
Compute the probability density function of a copula family.
Generate random samples from a copula family.
Randomly sample data.
Estimate the mean of the exponential probability distribution function from which sample data S has been taken.
Compute the negative log-likelihood of data under the exponential distribution with given parameter value.
Compute mean and variance of the exponential distribution.
Compute mean and variance of the F distribution.
Calculates the negative log-likelihood function for the Gamma distribution over vector R, with the given parameters A and B.
Compute mean and variance of the gamma distribution.
Compute mean and variance of the geometric distribution.
Compute the cumulative distribution function of the generalized extreme value (GEV) distribution.
Find the maximum likelihood estimator (PARAMHAT) of the generalized extreme value (GEV) distribution to fit DATA.
Find an estimator (PARAMHAT) of the generalized extreme value (GEV) distribution fitting DATA using the method of L-moments.
Compute a desired quantile (inverse CDF) of the generalized extreme value (GEV) distribution.
Compute the negative log-likelihood of data under the generalized extreme value (GEV) distribution with given parameter values.
Compute the probability density function of the generalized extreme value (GEV) distribution.
Return a matrix of random samples from the generalized extreme value (GEV) distribution with parameters K, SIGMA, MU.
Compute the mean and variance of the generalized extreme value (GEV) distribution.
Create an object of the gmdistribution class which represents a Gaussian mixture model with k components of n-dimensional Gaussians.
Compute the cumulative distribution function (CDF) at X of the generalized Pareto distribution with parameters LOCATION, SCALE, and SHAPE.
For each element of X, compute the quantile (the inverse of the CDF) at X of the generalized Pareto distribution with parameters LOCATION, SCALE, and SHAPE.
Compute the probability density function (PDF) at X of the generalized Pareto distribution with parameters LOCATION, SCALE, and SHAPE.
Return a matrix of random samples from the generalized Pareto distribution with parameters LOCATION, SCALE and SHAPE.
Compute mean and variance of the hypergeometric distribution.
Compute the probability density function of the Wishart distribution
Return a random matrix sampled from the inverse Wishart distribution with given parameters
For each element of X, compute the cumulative distribution function (CDF) at X of the Johnson SU distribution with shape parameters ALPHA1 and ALPHA2.
For each element of X, compute the probability density function (PDF) at X of the Johnson SU distribution with shape parameters ALPHA1 and ALPHA2.
Compute mean and variance of the lognormal distribution.
Compute the probability density function of the multinomial distribution.
Generate random samples from the multinomial distribution.
Compute multivariate normal pdf for X given mean MU and covariance matrix SIGMA.
Draw N random D-dimensional vectors from a multivariate Gaussian distribution with mean MU(NxD) and covariance matrix SIGMA(DxD).
Compute the cumulative distribution function of the multivariate normal distribution.
Compute the cumulative distribution function of the multivariate Student's t distribution.
Compute the probability density function of the multivariate Student's t distribution.
Generate random samples from the multivariate t-distribution.
For each element of X, compute the cumulative distribution function (CDF) at X of the Nakagami distribution with shape parameter M and scale parameter W.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Nakagami distribution with shape parameter M and scale parameter W.
For each element of X, compute the probability density function (PDF) at X of the Nakagami distribution with shape parameter M and scale parameter W.
Return a matrix of random samples from the Nakagami distribution with shape parameter M and scale W.
Compute mean and variance of the negative binomial distribution.
compute the non-central chi square probalitity density function at X , degree of freedom N , and non-centrality parameter LAMBDA .
Transform a set of data so as to be N(0,1) distributed according to an idea by van Albada and Robinson.
Compute mean and variance of the normal distribution.
Return probability density function of NAME function for value X.
Compute mean and variance of the Poisson distribution.
Returns random deviates drawn from a q-Gaussian distribution.
Generates pseudo-random numbers from a given one-, two-, or three-parameter distribution.
Elements sampled from a vector.
Compute the cumulative distribution function of the Rayleigh distribution.
Compute the quantile of the Rayleigh distribution.
Compute the probability density function of the Rayleigh distribution.
Generate a matrix of random samples from the Rayleigh distribution.
Compute mean and variance of the Rayleigh distribution.
Compute the cumulative distribution function (CDF) at X of the triangular distribution with parameters A, B, and C on the interval [A, B].
For each element of X, compute the quantile (the inverse of the CDF) at X of the triangular distribution with parameters A, B, and C on the interval [A, B].
Compute the probability density function (PDF) at X of the triangular distribution with parameters A, B, and C on the interval [A, B].
Return a matrix of random samples from the rectangular distribution with parameters A, B, and C on the interval [A, B].
Compute mean and variance of the t (Student) distribution.
Compute mean and variance of the discrete uniform distribution.
Compute mean and variance of the continuous uniform distribution.
Evaluates the Von Mises probability density function.
Draw random angles from a Von Mises distribution with mean MU and concentration K.
Compute mean and variance of the Weibull distribution.
Compute the probability density function of the Wishart distribution
Return a random matrix sampled from the Wishart distribution with given parameters
For each element of X, compute the cumulative distribution function (CDF) at X of the Beta distribution with parameters A and B.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Beta distribution with parameters A and B.
For each element of X, compute the probability density function (PDF) at X of the Beta distribution with parameters A and B.
Return a matrix of random samples from the Beta distribution with parameters A and B.
For each element of X, compute the cumulative distribution function (CDF) at X of the binomial distribution with parameters N and P, where N is the number of trials and P is the probability of succ...
For each element of X, compute the quantile (the inverse of the CDF) at X of the binomial distribution with parameters N and P, where N is the number of trials and P is the probability of success.
For each element of X, compute the probability density function (PDF) at X of the binomial distribution with parameters N and P, where N is the number of trials and P is the probability of success.
Return a matrix of random samples from the binomial distribution with parameters N and P, where N is the number of trials and P is the probability of success.
For each element of X, compute the cumulative distribution function (CDF) at X of the Cauchy distribution with location parameter LOCATION and scale parameter SCALE.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Cauchy distribution with location parameter LOCATION and scale parameter SCALE.
For each element of X, compute the probability density function (PDF) at X of the Cauchy distribution with location parameter LOCATION and scale parameter SCALE > 0.
Return a matrix of random samples from the Cauchy distribution with parameters LOCATION and SCALE.
For each element of X, compute the cumulative distribution function (CDF) at X of the chi-square distribution with N degrees of freedom.
For each element of X, compute the quantile (the inverse of the CDF) at X of the chi-square distribution with N degrees of freedom.
For each element of X, compute the probability density function (PDF) at X of the chi-square distribution with N degrees of freedom.
Return a matrix of random samples from the chi-square distribution with N degrees of freedom.
For each element of X, compute the cumulative distribution function (CDF) at X of the exponential distribution with mean LAMBDA.
For each element of X, compute the quantile (the inverse of the CDF) at X of the exponential distribution with mean LAMBDA.
For each element of X, compute the probability density function (PDF) at X of the exponential distribution with mean LAMBDA.
Return a matrix of random samples from the exponential distribution with mean LAMBDA.
For each element of X, compute the cumulative distribution function (CDF) at X of the F distribution with M and N degrees of freedom.
For each element of X, compute the quantile (the inverse of the CDF) at X of the F distribution with M and N degrees of freedom.
For each element of X, compute the probability density function (PDF) at X of the F distribution with M and N degrees of freedom.
Return a matrix of random samples from the F distribution with M and N degrees of freedom.
For each element of X, compute the cumulative distribution function (CDF) at X of the Gamma distribution with shape parameter A and scale B.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Gamma distribution with shape parameter A and scale B.
For each element of X, return the probability density function (PDF) at X of the Gamma distribution with shape parameter A and scale B.
Return a matrix of random samples from the Gamma distribution with shape parameter A and scale B.
For each element of X, compute the cumulative distribution function (CDF) at X of the geometric distribution with parameter P.
For each element of X, compute the quantile (the inverse of the CDF) at X of the geometric distribution with parameter P.
For each element of X, compute the probability density function (PDF) at X of the geometric distribution with parameter P.
Return a matrix of random samples from the geometric distribution with parameter P.
Compute the cumulative distribution function (CDF) at X of the hypergeometric distribution with parameters T, M, and N.
For each element of X, compute the quantile (the inverse of the CDF) at X of the hypergeometric distribution with parameters T, M, and N.
Compute the probability density function (PDF) at X of the hypergeometric distribution with parameters T, M, and N.
Return a matrix of random samples from the hypergeometric distribution with parameters T, M, and N.
Return the cumulative distribution function (CDF) at X of the Kolmogorov-Smirnov distribution.
For each element of X, compute the cumulative distribution function (CDF) at X of the Laplace distribution.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Laplace distribution.
For each element of X, compute the probability density function (PDF) at X of the Laplace distribution.
Return a matrix of random samples from the Laplace distribution.
For each element of X, compute the cumulative distribution function (CDF) at X of the logistic distribution.
For each element of X, compute the quantile (the inverse of the CDF) at X of the logistic distribution.
For each element of X, compute the PDF at X of the logistic distribution.
Return a matrix of random samples from the logistic distribution.
For each element of X, compute the cumulative distribution function (CDF) at X of the lognormal distribution with parameters MU and SIGMA.
For each element of X, compute the quantile (the inverse of the CDF) at X of the lognormal distribution with parameters MU and SIGMA.
For each element of X, compute the probability density function (PDF) at X of the lognormal distribution with parameters MU and SIGMA.
Return a matrix of random samples from the lognormal distribution with parameters MU and SIGMA.
For each element of X, compute the cumulative distribution function (CDF) at X of the negative binomial distribution with parameters N and P.
For each element of X, compute the quantile (the inverse of the CDF) at X of the negative binomial distribution with parameters N and P.
For each element of X, compute the probability density function (PDF) at X of the negative binomial distribution with parameters N and P.
Return a matrix of random samples from the negative binomial distribution with parameters N and P.
For each element of X, compute the cumulative distribution function (CDF) at X of the normal distribution with mean MU and standard deviation SIGMA.
For each element of X, compute the quantile (the inverse of the CDF) at X of the normal distribution with mean MU and standard deviation SIGMA.
For each element of X, compute the probability density function (PDF) at X of the normal distribution with mean MU and standard deviation SIGMA.
Return a matrix of random samples from the normal distribution with parameters mean MU and standard deviation SIGMA.
For each element of X, compute the cumulative distribution function (CDF) at X of the Poisson distribution with parameter LAMBDA.
For each element of X, compute the quantile (the inverse of the CDF) at X of the Poisson distribution with parameter LAMBDA.
For each element of X, compute the probability density function (PDF) at X of the Poisson distribution with parameter LAMBDA.
Return a matrix of random samples from the Poisson distribution with parameter LAMBDA.
For each element of X, compute the cumulative distribution function (CDF) at X of the standard normal distribution (mean = 0, standard deviation = 1).
For each element of X, compute the quantile (the inverse of the CDF) at X of the standard normal distribution (mean = 0, standard deviation = 1).
For each element of X, compute the probability density function (PDF) at X of the standard normal distribution (mean = 0, standard deviation = 1).
Return a matrix of random samples from the standard normal distribution (mean = 0, standard deviation = 1).
For each element of X, compute the cumulative distribution function (CDF) at X of the t (Student) distribution with N degrees of freedom.
For each element of X, compute the quantile (the inverse of the CDF) at X of the t (Student) distribution with N degrees of freedom.
For each element of X, compute the probability density function (PDF) at X of the T (Student) distribution with N degrees of freedom.
Return a matrix of random samples from the t (Student) distribution with N degrees of freedom.
For each element of X, compute the cumulative distribution function (CDF) at X of a discrete uniform distribution which assumes the integer values 1-N with equal probability.
For each element of X, compute the quantile (the inverse of the CDF) at X of the discrete uniform distribution which assumes the integer values 1-N with equal probability.
For each element of X, compute the probability density function (PDF) at X of a discrete uniform distribution which assumes the integer values 1-N with equal probability.
Return a matrix of random samples from the discrete uniform distribution which assumes the integer values 1-N with equal probability.
For each element of X, compute the cumulative distribution function (CDF) at X of the uniform distribution on the interval [A, B].
For each element of X, compute the quantile (the inverse of the CDF) at X of the uniform distribution on the interval [A, B].
For each element of X, compute the probability density function (PDF) at X of the uniform distribution on the interval [A, B].
Return a matrix of random samples from the uniform distribution on [A, B].
Compute the cumulative distribution function (CDF) at X of the Weibull distribution with scale parameter SCALE and shape parameter SHAPE.
Compute the quantile (the inverse of the CDF) at X of the Weibull distribution with scale parameter SCALE and shape parameter SHAPE.
Compute the probability density function (PDF) at X of the Weibull distribution with scale parameter SCALE and shape parameter SHAPE.
Return a matrix of random samples from the Weibull distribution with parameters SCALE and SHAPE.
Return a simulated realization of the D-dimensional Wiener Process on the interval [0, T].
Return all combinations of K elements in DATA.
Distance correlation, covariance and correlation statistics.
Compute the geometric mean.
Compute the harmonic mean.
Compute jackknife estimates of a parameter taking one or more given samples as parameters.
Find the maximal element while ignoring NaN values.
Compute the mean value while ignoring NaN values.
Compute the median of data while ignoring NaN values.
Find the minimal element while ignoring NaN values.
Compute the standard deviation while ignoring NaN values.
Compute the sum while ignoring NaN values.
Compute the variance while ignoring NaN values.
Compute the trimmed mean.
Compute a frequency table.
Return the complementary log-log function of X.
Create a cross-tabulation (contingency table) T from data vectors.
Compute the logit for each value of P
Return the probit (the quantile of the standard normal distribution) for each element of P.
Full factorial design.
Full-factor design with n binary terms.
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 the same distribution, i.e. the group ...
Perform a multi-way analysis of variance (ANOVA).
Canonical correlation analysis
Perform cross validation on given data.
Produce a smooth monotone increasing approximation to a sampled functional dependence
Performs a principal component analysis on a data matrix X
Perform principal component analysis on the nxn covariance matrix X
Calulate residuals from principal component analysis
Calculate partial least squares regression
Performs a principal component analysis on a NxP data matrix X
Multiple Linear Regression using Least Squares Fit of Y on X with the model 'y = X * beta + e'.
Linear scalar regression using gaussian processes.
This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the Li...
Produce a box plot.
Display a chart of a confusion matrix.
Plot a dendrogram of a hierarchical binary cluster tree.
Draw a scatter plot with grouped data.
Plot histogram with superimposed fitted normal density.
Produce bivariate (2D) histogram counts or plots.
Produce normal probability plot for each column of X.
Perform a repeated measures analysis of variance (Repeated ANOVA).
Compute the silhouette values of clustered data and show them on a plot.
Produce a Violin plot of the data X.
Plot a column vector DATA on a Weibull probability plot using rank regression.
Perform a PP-plot (probability plot).
Perform a QQ-plot (quantile plot).
Estimate the matrix of transition probabilities and the matrix of output probabilities of a given sequence of outputs and states generated by a hidden Markov model.
Generate an output sequence and hidden states of a hidden Markov model.
Use the Viterbi algorithm to find the Viterbi path of a hidden Markov model given a sequence of outputs.
Draws NSAMPLES samples from a target stationary distribution PDF using Metropolis-Hastings algorithm.
Draws NSAMPLES samples from a target stationary distribution PDF using slice sampling of Radford M.
Perform ordinal logistic regression.
Test the hypothesis that X is selected from the given distribution using the Anderson-Darling test.
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 gro...
Runs test for detecting serial correlation in the vector X.
Test for median.
Test for mean of a normal sample with unknown variance.
Test for mean of a normal sample with known variance.
Perform a F-test for equal variances.
Perform a F-test for equal variances.
Test for mean of a normal sample with known variance.
Perform a one-way analysis of variance (ANOVA).
Perform a Bartlett test for the homogeneity of variances in the data vectors X1, X2, ..., XK, where K > 1.
Given two samples X and Y, perform a chisquare test for homogeneity of the null hypothesis that X and Y come from the same distribution, based on the partition induced by the (strictly increasing) ...
Perform a chi-square test for independence based on the contingency table X.
Test whether two samples X and Y come from uncorrelated populations.
Perform an F test for the null hypothesis rr * b = r in a classical normal regression model y = X * b + e.
For a sample X from a multivariate normal distribution with unknown mean and covariance matrix, test the null hypothesis that 'mean (X) == M'.
For two samples X from multivariate normal distributions with the same number of variables (columns), unknown means and unknown equal covariance matrices, test the null hypothesis 'mean (X) == mean...
Perform a Kolmogorov-Smirnov test of the null hypothesis that the sample X comes from the (continuous) distribution DIST.
Perform a 2-sample Kolmogorov-Smirnov test of the null hypothesis that the samples X and Y come from the same (continuous) distribution.
Perform a Kruskal-Wallis one-factor analysis of variance.
Perform a one-way multivariate analysis of variance (MANOVA).
For a square contingency table X of data cross-classified on the row and column variables, McNemar's test can be used for testing the null hypothesis of symmetry of the classification probabilities.
If X1 and N1 are the counts of successes and trials in one sample, and X2 and N2 those in a second one, test the null hypothesis that the success probabilities P1 and P2 are the same.
Perform a chi-square test with 6 degrees of freedom based on the upward runs in the columns of X.
For two matched-pair samples X and Y, perform a sign test of the null hypothesis PROB (X > Y) == PROB (X < Y) == 1/2.
For a sample X from a normal distribution with unknown mean and variance, perform a t-test of the null hypothesis 'mean (X) == M'.
For two samples x and y from normal distributions with unknown means and unknown equal variances, perform a two-sample t-test of the null hypothesis of equal means.
Perform a t test for the null hypothesis 'RR * B = R' in a classical normal regression model 'Y = X * B + E'.
For two samples X and Y, perform a Mann-Whitney U-test of the null hypothesis PROB (X > Y) == 1/2 == PROB (X < Y).
For two samples X and Y from normal distributions with unknown means and unknown variances, perform an F-test of the null hypothesis of equal variances.
For two samples X and Y from normal distributions with unknown means and unknown and not necessarily equal variances, perform a Welch test of the null hypothesis of equal means.
For two matched-pair sample vectors X and Y, perform a Wilcoxon signed-rank test of the null hypothesis PROB (X > Y) == 1/2.
Perform a Z-test of the null hypothesis 'mean (X) == M' for a sample X from a normal distribution with unknown mean and known variance V.
For two samples X and Y from normal distributions with unknown means and known variances V_X and V_Y, perform a Z-test of the hypothesis of equal means.
Fit a Gaussian mixture model with K components to DATA.
Calculate gamma distribution parameters.
Define clusters from an agglomerative hierarchical cluster tree.
Wrapper function for 'linkage' and 'cluster'.
Classical multidimensional scaling of a matrix.
Compute the cophenetic correlation coefficient.
Create a clustering evaluation object to find the optimal number of clusters.
Compute the inconsistency coefficient for each link of a hierarchical cluster tree.
Perform a K-means clustering of the NxD table DATA.
Produce a hierarchical clustering dendrogram
Mahalanobis' D-square distance.
Compute the optimal leaf ordering of a hierarchical binary cluster tree.
Return the distance between any two rows in X.
Compute pairwise distance between two sets of vectors.
Interchange between distance matrix and distance vector formats.
Read case names from an ascii file.
Write case names to an ascii file.
Read tabular data from an ascii file.
Write tabular data to an ascii file.
Create a partition object for cross validation.
Display a cvpartition object.
Get a field from a 'cvpartition' object.
Return a new cvpartition object.
Set field(s) in a 'cvpartition' object.
Return logical vector for testing-subset indices from a cvpartition object.
Return logical vector for training-subset indices from a cvpartition object.
Get index for group variables.
Display a chart of a confusion matrix.
Compute a confusion matrix for classification problems
Calculates 2*N+1 sigma points in N dimensions.
Find missing data in a matrix or a string array.
Remove missing or incomplete data from an array or a matrix.
Package: statistics