Functions and CALL Routines

# 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)

### 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

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) (See References) is used. For a 1, an acceptance-rejection method due to Fishman is used (1978, Algorithm G2) (See References).

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.

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

 Functions and CALL routines:

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