(Scaled) Inverse Chi-Squared Distribution
This is the density function and random generation for the (scaled) inverse chi-squared distribution.
This is a vector of quantiles.
This is the number of observations. If
This is the degrees of freedom parameter, usually represented as nu.
This is the scale parameter, usually represented as lambda.
Application: Continuous Univariate
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.
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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"))
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