InvChisquare | R Documentation |
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
.
dinvchisq(x, df, scale, log = FALSE) rinvchisq(n, df, scale = 1/df)
x |
vector of quantiles. |
n |
number of observations. If |
df |
degrees of freedom. |
scale |
scale parameter. |
log |
logical; if TRUE, densities d are given as log(d). |
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.
dinvchisq
gives the density and rinvchisq
generates random deviates.
rchisq
for the chi-squared distribution which
is the basis for this function.
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))
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