# RANGAM Function

Returns a random variate from a gamma distribution.

 Category: Random Number Tip: If you want to change the seed value during execution, you must use the CALL RANGAM routine instead of the RANGAM function.

## Syntax

RANGAM(seed,a)

### Required Arguments

#### seed

is a numeric constant, variable, or expression with an integer value. If seed ≤ 0, the time of day is used to initialize the seed stream.

#### a

is a numeric constant, variable, or expression that specifies the shape parameter.

 Range a > 0

## Details

The RANGAM function returns a variate that is generated from a gamma distribution with parameter a. For a > 1, an acceptance-rejection method due to Cheng (1977) is used. (See For a ≤ 1, an acceptance-rejection method due to Fishman is used (1978, Algorithm G2) (See
A gamma variate X with shape parameter ALPHA and scale BETA can be generated:
`x=beta*rangam(seed,alpha);`
If 2*ALPHA is an integer, a chi-square variate X with 2*ALPHA degrees of freedom can be generated:
`x=2*rangam(seed,alpha);`
If N is a positive integer, an Erlang variate X can be generated:
`x=beta*rangam(seed,N);`
It has the distribution of the sum of N independent exponential variates whose means are BETA.
And finally, a beta variate X with parameters ALPHA and BETA can be generated:
```y1=rangam(seed,alpha);
y2=rangam(seed,beta);
x=y1/(y1+y2);```
For a discussion about seeds and streams of data, as well as examples of using the random-number functions, see Generating Multiple Variables from One Seed in Random-Number Functions.

## Comparisons

The CALL RANGAM routine, an alternative to the RANGAM function, gives greater control of the seed and random number streams.