(Scaled) Inverse Chi-Squared Distribution
This is the density function and random generation for the (scaled) inverse chi-squared distribution.
dinvchisq(x, df, scale, log=FALSE) rinvchisq(n, df, scale=1/df)
x |
This is a vector of quantiles. |
n |
This is the number of observations. If |
df |
This is the degrees of freedom parameter, usually represented as nu. |
scale |
This is the scale parameter, usually represented as lambda. |
log |
Logical. If |
Application: Continuous Univariate
Density:
p(theta) = ((nu/2)^(nu/2))/(Γ(nu/2)) lambda^nu (1/theta)^((nu/2)+1) exp(-(nu lambda^2)/(2*theta)), theta >= 0
Inventor: Derived from the chi-squared distribution
Notation 1: theta ~ chi^(-2)(nu, lambda)
Notation 2: p(theta) = chi^(-2)(theta | nu, lambda)
Parameter 1: degrees of freedom parameter nu > 0
Parameter 2: scale parameter lambda
Mean: E(theta) = unknown
Variance: var(theta) = unknown
Mode: mode(theta) =
The inverse chi-squared distribution, also called the inverted chi-square distribution, is the multiplicate inverse of the chi-squared distribution. If x has the chi-squared distribution with nu degrees of freedom, then 1 / x has the inverse chi-squared distribution with nu degrees of freedom, and nu / x has the inverse chi-squared distribution with nu degrees of freedom.
These functions are similar to those in the GeoR package.
dinvchisq gives the density and
rinvchisq generates random deviates.
library(LaplacesDemon)
x <- dinvchisq(1,1,1)
x <- rinvchisq(10,1)
#Plot Probability Functions
x <- seq(from=0.1, to=5, by=0.01)
plot(x, dinvchisq(x,0.5,1), ylim=c(0,1), type="l", main="Probability Function",
ylab="density", col="red")
lines(x, dinvchisq(x,1,1), type="l", col="green")
lines(x, dinvchisq(x,5,1), type="l", col="blue")
legend(3, 0.9, expression(paste(nu==0.5, ", ", lambda==1),
paste(nu==1, ", ", lambda==1), paste(nu==5, ", ", lambda==1)),
lty=c(1,1,1), col=c("red","green","blue"))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.