Igamma {UCS} R Documentation

## The Incomplete Gamma Function (sfunc)

### Description

Computes the incomplete Gamma function and its inverse. Both the lower and the upper incomplete Gamma function are supported, and the Gamma value can be scaled to a base 10 logarithm.

### Usage

```Igamma(a, x, lower=TRUE, log=FALSE)

Igamma.inv(a, y, lower=TRUE, log=FALSE)
```

### Arguments

 `a` a non-negative numeric vector, the parameter of the incomplete Gamma function `x` a non-negative numeric vector, the point at which the incomplete Gamma function is evaluated `y` a numeric vector, the values of the incomplete Gamma function (or their base 10 logarithms if `log=TRUE`) `lower` if `TRUE`, computes the lower incomplete Gamma function (default). Otherwise, computes the upper incomplete Gamma function. `log` if `TRUE`, the Gamma values are base 10 logarithms (default: `FALSE`)

### Details

The upper incomplete Gamma function is defined by the Gamma integral

Gamma(a,x) = integral_x^Inf t^(a-1) exp(-t) dt

The lower incomplete Gamma function is defined by the complementary Gamma integral

gamma(a,x) = integral_0^x t^(a-1) exp(-t) dt

### Value

`Igamma` returns the (lower or upper) incomplete Gamma function with parameter `a` evaluated at point `x`.

`Igamma.inv` returns the point `x` at which the (lower or upper) incomplete Gamma function with parameter `a` evaluates to `y`.

`Cgamma`, `Rgamma`, `Cbeta`, `Ibeta`, `Rbeta`