R: The (Scaled) Inverse Chi-Squared Distribution

InvChisquare {geoR} | R Documentation

## The (Scaled) Inverse Chi-Squared Distribution

### Description

Density and random generation for the scaled inverse chi-squared (chi^2_{ScI}) distribution with `df` degrees of freedom and optional non-centrality parameter `scale`.

### Usage

    dinvchisq(x, df, scale, log = FALSE)
    rinvchisq(n, df, scale = 1/df)

### Arguments

`x` | vector of quantiles.
`n` | number of observations. If `length(n) > 1`, the length is taken to be the number required.
`df` | degrees of freedom.
`scale` | scale parameter.
`log` | logical; if TRUE, densities d are given as log(d).

### Details

The inverse chi-squared distribution with `df`= n degrees of freedom has density

f(x) = 1 / (2^(n/2) Gamma(n/2)) (1/x)^(n/2-1) e^(-1/(2x))

for x > 0. The mean and variance are 1/(n-2) and 2/((n-4)(n-2)^2).

The non-central chi-squared distribution with `df`= n degrees of freedom and non-centrality parameter `scale` = S^2 has density

f(x) = ((n/2)^(n/2))/(Γ (n/2)) S^n (1/x)^((n/2)+1) e^(-(n S^2)/(2x))

, for x ≥ 0. The first is a particular case of the latter for λ = n/2.

### Value

`dinvchisq` gives the density and `rinvchisq` generates random deviates.

### See Also

`rchisq` for the chi-squared distribution which is the basis for this function.

### Examples

    set.seed(1234); rinvchisq(5, df=2)
    set.seed(1234); 1/rchisq(5, df=2)

    set.seed(1234); rinvchisq(5, df=2, scale=5)
    set.seed(1234); 5*2/rchisq(5, df=2)

    ## inverse Chi-squared is a particular case
    x <- 1:10
    all.equal(dinvchisq(x, df=2), dinvchisq(x, df=2, scale=1/2))

[Package geoR version 1.7-5.2 Index]