**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.

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

`install.packages("invgamma")`

For the development version, use

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

`(d/p/q/r)invgamma()`

functionsThe 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())
<- seq(0, 5, .01)
x 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:

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

```
<- rinvgamma(1e5, 7, 10)
samples 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")
```

`(d/p/q/r)invchisq()`

and `(d/p/q/r)invexp()`

functionsThe gamma
distribution subsumes the chi-squared
and exponential
distributions,
so it makes sense to include the `*invchisq()`

and
`*invexp()`

functions in **invgamma**. Their
implementations, however, wrap `*chisq()`

and
`*exp()`

, not `*invgamma()`

.