RANCAU Function

Returns a random variate from a Cauchy distribution.

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

Syntax

RANCAU(seed)

Required Argument

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.

Range	seed < 2³¹ −1
See	Seed Values for more information about seed values

Details

The RANCAU function returns a variate that is generated from a Cauchy distribution with location parameter 0 and scale parameter 1. An acceptance-rejection procedure applied to RANUNI uniform variates is used. If u and v are independent uniform (−1/2, 1/2) variables and

u^{2} + v^{2} \leq 1 / 4

, then u/v is a Cauchy variate. A Cauchy variate X with location parameter ALPHA and scale parameter BETA can be generated:

x=alpha+beta*rancau(seed);

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