dinvrootgamma: Inverse root gamma distribution

Description Usage Arguments Details Value See Also

Description

If X ~ InvRootGamma(scale=sigma.sq, df=nu), then 1/(X^2) ~ Gamma(shape=nu/2, rate=nu*sigma.sq/2).

Usage

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dinvrootgamma(x, shape, df, log = FALSE)

rinvrootgamma(n, shape, df)

pinvrootgamma(q, shape, df, log = FALSE)

Arguments

x

vector of quantiles

shape

parameter, where shape>0

df

degrees of freedom parameter, where df>0

log

logical; if TRUE, probabilities p are given as log(p).

n

number of random deviates to draw

q

vector of quantiles

Details

The density function of the inverse-root-gamma distribution shape σ^2 and ν degrees of freedom is

p(θ) = I(θ>0)\frac{2}{Γ≤ft(\frac{ν}{2}\right)} ≤ft( \frac{νσ^2}{2}\right)^{ν/2}\frac{1}{θ^{ν+1}} \exp≤ft\{-\frac{ν σ^2}{2θ^2}\right\}.

The cdf is

P(x) = \frac{Γ ≤ft(\frac{ν }{2},\frac{ν σ ^2}{2 x^2}\right)}{Γ ≤ft(\frac{ν }{2}\right)}.

Note that some authors use alternative parameterizations; see especially dinvgamma.

Value

'dinvgamma' gives the density and 'rinvgamma' generates random deviates.

See Also

Other gamma: dinvgamma


kuperov/bdist documentation built on May 23, 2019, 7:20 a.m.