The Inverse Gamma Distribution.

invgamma

invgamma implements the (d/p/q/r) statistics functions for the inverse gamma distribution in R. It is ideal for using in other packages since it is lightweight and leverages the (d/p/q/r)gamma() line of functions maintained by CRAN.

Getting invgamma

There are two ways to get invgamma. For the CRAN version, use

install.packages("invgamma")

For the development version, use

# install.packages("devtools")
devtools::install_github("dkahle/invgamma")

The (d/p/q/r)invgamma() functions

The functions in invgamma match those for the gamma distribution provided by the stats package. Namely, it uses as its density f(x) = (b^a / Gamma(a)) x^-(a+1) e^(-b/x), where a = shape and b = rate.

The PDF (the f(x) above) can be evaluated with the dinvgamma() function:

library(invgamma)
library(ggplot2); theme_set(theme_bw())
x <- seq(0, 5, .01)
qplot(x, dinvgamma(x, 7, 10), geom = "line")
#  Warning: Removed 1 rows containing missing values (geom_path).

The CDF can be evaluated with the pinvgamma() function:

f <- function(x) dinvgamma(x, 7, 10)
q <- 2
integrate(f, 0, q)
#  0.7621835 with absolute error < 7.3e-05
(p <- pinvgamma(q, 7, 10))
#  [1] 0.7621835

The quantile function can be evaluated with qinvgamma():

qinvgamma(p, 7, 10) # = q
#  [1] 2

And random number generation can be performed with rinvgamma():

set.seed(1)
rinvgamma(5, 7, 10)
#  [1] 1.9996157 0.9678268 0.9853343 1.3157697 3.1578177

rinvgamma() can be used to obtain a Monte Carlo estimate of the probability given by pinvgamma() above:

samples <- rinvgamma(1e5, 7, 10)
mean(samples <= q)
#  [1] 0.7621

Moreover, we can check the consistency and correctness of the implementation with

qplot(samples, geom = "density") + 
  stat_function(fun = f,  color = "red")

The (d/p/q/r)invchisq() and (d/p/q/r)invexp() functions

The gamma distribution subsumes the chi-squared and exponentialdistributions, so it makes sense to include the *invchisq() and *invexp() functions in invgamma. Their implementations, however, wrap *chisq() and *exp(), not *invgamma().