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