# Statistical distributions and sampling¶

## Cumulative distributions¶

 cdfBeta Computes integral of beta function. cdfBetaInv Computes the quantile or inverse of the beta cumulative distribution function. cdfBinomial Computes the binomial cumulative distribution function. cdfBinomialInv Computes the binomial quantile or inverse cumulative distribution function. cdfBvn Computes lower tail of bivariate Normal cdf. cdfBvn2 Returns cdfbvn of a bounded rectangle. cdfBvn2e Returns cdfbvn of a bounded rectangle and error estimates. cdfCauchy Computes the cumulative distribution function for the Cauchy distribution. cdfCauchyInv Computes the Cauchy inverse cumulative distribution function. cdfChic Computes complement of cdf of $$\chi^2$$. cdfChii Computes $$\chi^2$$ abscissae values given probability and degrees of freedom. cdfChinc Computes integral of noncentral $$\chi^2$$. cdfEmpirical Computes the cumulative distribution function for the empirical distribution. cdfExp Computes the cumulative distribution function for the exponential distribution. cdfExpInv Computes the exponential inverse cumulative distribution function. cdfFc Computes complement of cdf of F. cdfFnc Computes integral of noncentral F. cdfFncInv Computes the quantile or inverse of noncentral F cumulative distribution function. cdfGam Computes integral of incomplete gamma function. cdfGenPareto Computes the cumulative distribution function for the Generalized Pareto distribution. cdfHyperGeo Computes the cumulative distribution function of the hypergeometric distribution. cdfLaplace Computes the cumulative distribution function for the Laplace distribution. cdfLaplaceInv Computes the Laplace inverse cumulative distribution function. cdfLogNorm Computes the cumulative distribution function of the log-normal distribution. cdfMvn Computes multivariate Normal cdf. cdfMvnce Computes the complement of the multivariate Normal cumulative distribution function with error management cdfMvne Computes multivariate Normal cumulative distribution function with error management cdfMvn2e Computes the multivariate Normal cumulative distribution function with error management over the range $$[a,b]$$ cdfMvtce Computes complement of multivariate Student’s t cumulative distribution function with error management cdfMvte Computes multivariate Student’s t cumulative distribution function with error management cdfMvt2e Computes multivariate Student’s t cumulative distribution function with error management over $$[a,b]$$ cdfn, cdfnc Computes integral (or complement) of Normal distribution: lower tail, or cdf. cdfN2 Computes interval of Normal cdf. cdfNegBinomial Computes the cumulative distribution function for the negative binomial distribution. cdfNegBinomialInv Computes the quantile or inverse negative binomial cumulative distribution function. cdfni Computes the inverse of the cdf of the Normal distribution. cdfPoisson Computes the Poisson cumulative distribution function. cdfPoissonInv Computes the quantile or inverse Poisson cumulative distribution function. cdfRayleigh Computes the Rayleigh cumulative distribution function. cdfRayleighInv Computes the Rayleigh inverse cumulative distribution function. cdfTc Computes complement of cdf of t-distribution. cdfTci Computes the inverse of the complement of the Student’s t cdf. cdfTnc Computes integral of noncentral t-distribution. cdfTvn Computes lower tail of trivariate Normal cdf. cdfTruncNorm Computes the cumulative distribution function of the normal distibution over the interval from a to b. cdfWeibull Computes the cumulative distribution function for the Weibull distribution. cdfWeibullInv Computes the Weibull inverse cumulative distribution function. erf, erfc Computes the Gaussian error function, or its complement. erfcplx, erfccplx Computes the Gaussian error function for complex inputs or its complement. lncdfbvn Computes natural log of bivariate Normal cdf. lncdfbvn2 Returns log of cdfbvn of a bounded rectangle. lncdfmvn Computes natural log of multivariate Normal cdf. lncdfn Computes natural log of Normal cdf. lncdfn2 Computes natural log of interval of Normal cdf. lncdfnc Computes natural log of complement of Normal cdf.

## Probability density and mass¶

 lnpdfmvn Computes multivariate Normal log-probabilities. lnpdfmvt Computes multivariate Student’s t log-probabilities. lnpdfn Computes Normal log-probabilities. lnpdft Computes Student’s t log-probabilities. pdfBinomial Computes the probability mass function for the binomial distribution. pdfCauchy Computes the probability density function for the Cauchy distribution. pdfexp Computes the probability density function for the exponential distribution. pdfGenPareto Computes the probability density function for the Generalized Pareto distribution. pdfHyperGeo Computes the probability mass function for the hypergeometric distribution. pdfLaplace Computes the probability density function for the Laplace distribution. pdflogistic Computes the probability density function for the logistic distribution. pdfLogNorm Computes the probability density function of the log-normal distribution. pdfn Computes standard Normal probability density function. pdfPoisson Computes the probability mass function for the Poisson distribution. pdfRayleigh Computes the probability density function of the Rayleigh distribution. pdfTruncNorm Computes the cumulative distribution function of the normal distribution over the interval from a to b. pdfWeibull Computes the probability density function of a Weibull random variable. pdfWishartInv Computes the probability density function of a inverse Wishart distribution.

## Random Numbers¶

 rndBernoulli Computes random numbers with Bernoulli distribution. rndBeta Computes random numbers with beta distribution. rndBinomial Computes binomial pseudo-random numbers with the choice of underlying random number generator. rndCauchy Computes Cauchy distributed random numbers with a choice of underlying random number generator. rndChiSquare Creates pseudo-random numbers with a chi-squared distribution, with an optional non-centrality parameter and a choice of underlying random number generator. rndCreateState Creates a new random number stream for a specified generator type from a seed value. rndExp Computes exponentially distributed random numbers with a choice of underlying random number generator. rndGamma Computes gamma pseudo-random numbers with a choice of underlying random number generator. rndGeo Computes geometric pseudo-random numbers with a choice of underlying random number generator. rndGumbel Computes Gumbel distributed random numbers with a choice of underlying random number generator. rndHyperGeo Computes pseudo-random numbers following a hypergeometric distribution with a choice of underlying random number generator. rndi Returns random integers in a specified range. rndKMvm Computes von Mises pseudo-random numbers. rndLaplace Computes Laplacian pseudo-random numbers with the choice of underlying random number generator. rndLogNorm Computes lognormal pseudo-random numbers with the choice of underlying random number generator. rndMVn Computes multivariate normal random numbers given a covariance matrix. rndMVt Computes multivariate Student-t random numbers given a covariance matrix. rndn Computes normally distributed pseudo-random numbers with a choice of underlying random number generator. rndNegBinomial Computes negative binomial pseudo-random numbers with a choice of underlying random number generator. rndPoisson Computes Poisson pseudo-random numbers with a choice of underlying random number generator. rndRayleigh Computes Rayleigh pseudo-random numbers with the choice of underlying random number generator. rndseed Changes seed of the random number generator. rndStateSkip Used to skip ahead in a random number sequence. rndu Computes uniform random numbers with a choice of underlying random number generator. rndWeibull Computes Weibull pseudo-random numbers with the choice of underlying random number generator. rndWishart Computes Wishart pseudo-random matrices with the choice of underlying random number generator. rndWishartInv Computes inverse Wishart pseudo-random matrices with the choice of underlying random number generator.

## Sampling¶

 sampleData Returns a sample of the rows of a dataframe or matrix, chosen with or without replacement