Math::Random has a bunch of rng's with nonlinear distributions.

Hi kingkongrevenge

The book Mastering Algorithms with Perl by Jon Orwant, Jarkko Hietaniemi, and John Macdonald provides the code to compute several probability distributions (the geometric distribution included). The source code is available at http://examples.oreilly.com/maperl/ (once you uncompress the file, the code will be in the file "distributions" inside the ch14 folder).

I hope this helps.

Cheers,

    use Math::Trig; # to get PI
    my $sinerand = sin( rand() * PI );
[download]

A simple integration is also needed for the triangular distribution: Its probability density function has a smooth gradient so the generator satisfies the equation dy/dx = gradient. So integrating that straight line function, gives the generating function: 1 - (rand() ** (1+gradient))) would give a random number with a triangular probability density function coming out.

The reason the normal distribution is an exception deserving a special method is that its cumulative distribution function isn't analytic but can only be expressed as an integral equation. (Update: or as a Taylor Series.) You would need to achieve an impossible integration (in closed form) to compute the generating function that can produce a normal probability density function as its output. In practice some kind of approximation has to be used (Update: usually by taking the first few terms of the infinite Taylor series - although I have to say the module either doesn't or doesn't obviously do that!)

• PDL::GSL::RNG
• PDL::GSL::INTEG