Rgamma {UCS} R Documentation

## The Regularized Gamma Function (sfunc)

### Description

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

### Usage

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

Rgamma.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 regularized Gamma function (or their base 10 logarithms if `log=TRUE`) `lower` if `TRUE`, computes the lower regularized Gamma function (default). Otherwise, computes the upper regularized Gamma function. `log` if `TRUE`, the Gamma values are base 10 logarithms (default: `FALSE`)

### Details

The regularized Gamma functions scale the corresponding incomplete Gamma functions to the interval [0,1], by dividing through Γ(a). Thus, the lower regularized Gamma function is given by

P(a,x) = gamma(a,x) / Gamma(a)

and the upper regularized Gamma function is given by

Q(a,x) = Gamma(a,x) / Gamma(a)

### Value

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

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

`Cgamma`, `Igamma`, `Cbeta`, `Ibeta`, `Rbeta`
```## P(X >= k) for Poisson distribution with mean alpha