GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

# 19 Random Number Distributions

This chapter describes functions for generating random variates and computing their probability distributions. Samples from the distributions described in this chapter can be obtained using any of the random number generators in the library as an underlying source of randomness.

In the simplest cases a non-uniform distribution can be obtained
analytically from the uniform distribution of a random number generator
by applying an appropriate transformation. This method uses one call to
the random number generator. More complicated distributions are created
by the *acceptance-rejection* method, which compares the desired
distribution against a distribution which is similar and known
analytically. This usually requires several samples from the generator.

The library also provides cumulative distribution functions and inverse cumulative distribution functions, sometimes referred to as quantile functions. The cumulative distribution functions and their inverses are computed separately for the upper and lower tails of the distribution, allowing full accuracy to be retained for small results.

The functions for random variates and probability density functions
described in this section are declared in `‘gsl_randist.h’`. The
corresponding cumulative distribution functions are declared in
`‘gsl_cdf.h’`.

Note that the discrete random variate functions always
return a value of type `unsigned int`

, and on most platforms this
has a maximum value of
2^32-1 ~=~ 4.29e9. They should only be called with
a safe range of parameters (where there is a negligible probability of
a variate exceeding this limit) to prevent incorrect results due to
overflow.

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |