dist.Inverse.ChiSquare | R Documentation |
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 |
scale |
This is the scale parameter, usually represented as
|
log |
Logical. If |
Application: Continuous Univariate
Density:
p(\theta) = \frac{{\nu/2}^{\nu/2}}{\Gamma(\nu/2)}
\lambda^\nu \frac{1}{\theta}^{\nu/2+1} \exp(-\frac{\nu
\lambda^2}{2\theta}), \theta \ge 0
Inventor: Derived from the chi-squared distribution
Notation 1: \theta \sim \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.
dchisq
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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