## 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`.

### Function 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 8

       22.7804   11.5514   16.8537   12.7457   16.2303   10.7442   19.3942   16.3611

     Columns 9 to 9

       17.4772

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

    ans =

     Columns 1 to 8

       14.6404   15.1860   13.3147   11.4380    7.2307   10.8225   14.5271   12.4631

     Columns 9 to 9

       11.8753