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### Re: geometric random distributions

by Moron (Curate)
 on Jun 08, 2007 at 07:18 UTC ( #619971=note: print w/ replies, xml ) Need Help??

in reply to geometric random distributions

It's usually a trivial matter to create a geometric random number generator. For example, this expression will produce a random number in the range 0 to 1 with a (update co-)sinusoidal probability density function:

```    use Math::Trig; # to get PI
my \$sinerand = sin( rand() * PI );
(update: the probability density function of a random number generator is the derivative of the generating function, so in this case a cosine density shape is therefore being produced.)

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!)

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