Pseudorandom Number Generator - Non-uniform Generators

Non-uniform Generators

Numbers selected from a non-uniform probability distribution can be generated using a uniform distribution PRNG and a function that relates the two distributions.

First, one needs the cumulative distribution function of the target distribution :

Note that . Using a random number c from a uniform distribution as the probability density to "pass by", we get

so that

is a number randomly selected from distribution .

For example, the inverse of cumulative Gaussian distribution with an ideal uniform PRNG with range (0, 1) as input would produce a sequence of (positive only) values with a Gaussian distribution; however

• when using practical number representations, the infinite "tails" of the distribution have to be truncated to finite values.
• Repetitive recalculation of should be reduced by means such as ziggurat algorithm for faster generation.

Similar considerations apply to generating other non-uniform distributions such as Rayleigh and Poisson.