invgamma {contextual} R Documentation

## The Inverse Gamma Distribution

### Description

Density, distribution function, quantile function and random generation for the inverse gamma distribution.

### Usage

```dinvgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)

pinvgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)

qinvgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)

rinvgamma(n, shape, rate = 1, scale = 1/rate)
```

### Arguments

 `x, q` vector of quantiles. `shape` inverse gamma shape parameter `rate` inverse gamma rate parameter `scale` alternative to rate; scale = 1/rate `log, log.p` logical; if TRUE, probabilities p are given as log(p). `lower.tail` logical; if TRUE (default), probabilities are P(X <= x) otherwise, P(X > x). `p` vector of probabilities. `n` number of observations. If length(n) > 1, the length is taken to be the number required.

### Details

The inverse gamma distribution with parameters shape and rate has density f(x) = rate^shape/Gamma(shape) x^(-1-shape) e^(-rate/x) it is the inverse of the standard gamma parameterization in R.

The functions (d/p/q/r)invgamma simply wrap those of the standard (d/p/q/r)gamma R implementation, so look at, say, `dgamma` for details.

### Examples

```
s <- seq(0, 5, .01)
plot(s, dinvgamma(s, 7, 10), type = 'l')

f <- function(x) dinvgamma(x, 7, 10)
q <- 2
integrate(f, 0, q)
(p <- pinvgamma(q, 7, 10))
qinvgamma(p, 7, 10) # = q
mean(rinvgamma(1e5, 7, 10) <= q)
```

[Package contextual version 0.9.8.4 Index]