FreeMat: RANDGAMMA Generate Gamma-Distributed Random Variable

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RANDGAMMA Generate Gamma-Distributed Random Variable

Section: Random Number Generation

# Usage

Generates random variables with a gamma distribution. The general syntax for its use is

       y = randgamma(a,r),

where `a` and `r` are vectors describing the parameters of the gamma distribution. Roughly speaking, if `a` is the mean time between changes of a Poisson random process, and we wait for the `r` change, the resulting wait time is Gamma distributed with parameters `a` and `r`.

# Internals

The Gamma distribution arises in Poisson random processes. It represents the waiting time to the occurance of the `r`-th event in a process with mean time `a` between events. The probability distribution of a Gamma random variable is

Note also that for integer values of `r` that a Gamma random variable is effectively the sum of `r` exponential random variables with parameter `a`.

# Example

Here we use the `randgamma` function to generate Gamma-distributed random variables, and then generate them again using the `randexp` function.

    --> randgamma(1,15*ones(1,9))

    ans =

     Columns 1 to 7

       10.0227   12.4783   18.0388   21.7056   14.1249   15.9260   22.0177

     Columns 8 to 9

       15.9170   24.3781

    --> sum(randexp(ones(15,9)))

    ans =

     Columns 1 to 7

       14.5031   12.8908   10.5201   16.9976    9.8463   12.7479   13.6879

     Columns 8 to 9

       21.7005   11.4172