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geometric random distributions

by kingkongrevenge (Scribe)
on Jun 08, 2007 at 03:24 UTC ( #619944=perlquestion: print w/ replies, xml ) Need Help??
kingkongrevenge has asked for the wisdom of the Perl Monks concerning the following question:

boost::random for C++ has a bunch of classes for making random numbers with non-linear distributions: docs. You can get random numbers biased on a normal, triangle, or geometric distribution, for examples.

I can only find linear and normal distribution type random distribution modules on CPAN. If the geometric distribution equivalent exists, I don't understand how I'm supposed to find it. Does it exist? If not I guess I might write my first CPAN module.

Comment on geometric random distributions
Re: geometric random distributions
by Zaxo (Archbishop) on Jun 08, 2007 at 03:35 UTC

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

    After Compline,
    Zaxo

Re: geometric random distributions
by lin0 (Curate) on Jun 08, 2007 at 03:47 UTC
Re: geometric random distributions
by Moron (Curate) on Jun 08, 2007 at 07:18 UTC
    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!)

    __________________________________________________________________________________

    ^M Free your mind!

Re: geometric random distributions
by injunjoel (Priest) on Jun 08, 2007 at 16:41 UTC
    You might want to look into PDL as well.
    These are just a few of the modules available.

    -InjunJoel
    "I do not feel obliged to believe that the same God who endowed us with sense, reason and intellect has intended us to forego their use." -Galileo
Re: geometric random distributions
by silverrock (Initiate) on Aug 22, 2011 at 03:37 UTC
    int(log(1- rand)/log(1 - $p)) will give you a random integer from a geometric distribution with probability $p. $p must, of course, be between 0 and 1.

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