MultivariateSpecial: Multivariate special functions

Description Usage Arguments Details Value Note Author(s) See Also Examples

Description

Special matematical functions related to the multivariate gamma function which appears in the Wishart and Inverse Wishart distributions. The interface and usage should mirror the Special mathematical functions from the base package.

Usage

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gammap(x, p = 1)

digammap(x, p = 1)

Dgammap(x, p = 1)

psigammap(x, p = 1, deriv = 0)

trigammap(x, p = 1, deriv = 0)

lgammap(x, p = 1L)

Arguments

x

A numeric vector of values. The values of x should be strictly greater than (p - 1)/2.

p

A (single) integer giving the dimension. Default is 1.

deriv

A (single) integer giving the order of the derivative. Default is 0.

Details

Warnings are thown when the functions are evaluated outside its domain. Run Bmisc:::plotMultivariateSpecial() for more info.

Value

Returns a numeric vector with the same length as x. Similar to gamma and related functions NaNs are returned with warning when the function is evaluated outside its domain

gammap is the multivariate gamma function.

digammap is the multivariate digamma function.

Dgammap is the derivative of the multivariate gamma function.

psigammap is the n'th derivative log multivariate gamma function (i.e. multivariate polygamma).

trigammap is the 2'nd derivative log multivariate gamma function (i.e. the multivariate trigamma).

lgammap is the log multivariate gamma function.

Note

For lgammp, warnings of the type "value out of range in 'lgamma'" is due to evaluation in the half integers below (p-1)/2.

Author(s)

Anders Ellern Bilgrau <anders.ellern.bilgrau (at) gmail.com>

See Also

The Special mathematical functions.

Examples

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gammap(3.2, p = 1)
gammap(c(0.2, 0.5, 0.9, 1.2, 1.5), p = 3)   # x < (p-1)/2  !
lgammap(3.1, p = 2)
digammap(2, p = 3)
Dgammap(3.2, p = 1)

# A plot of all special functions
Bmisc:::plotMultivariateSpecial()

AEBilgrau/Bmisc documentation built on Jan. 17, 2019, 10:10 a.m.