InvChisquare: The (Scaled) Inverse Chi-Squared Distribution In geoR: Analysis of Geostatistical Data

 InvChisquare 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.

`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))
```

geoR documentation built on Aug. 9, 2022, 5:11 p.m.