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 distibution 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