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Subsections

RANDGAMMA Generate Gamma-Distributed Random Variable

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

$\displaystyle P(x) = \frac{a^r x^{r-1} e^{-ax}}{\Gamma(r)}.
$

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 = 
  <float>  - size: [1 9]
 
Columns 1 to 3
   18.003479          18.014494          22.860670        
 
Columns 4 to 6
   18.482702          15.879181          14.020444        
 
Columns 7 to 9
   18.032330          18.265949          10.394668        
--> sum(randexp(ones(15,9)))
ans = 
  <float>  - size: [1 9]
 
Columns 1 to 3
   21.299023          18.793451          16.707335        
 
Columns 4 to 6
   16.798256          14.229127          14.662329        
 
Columns 7 to 9
   16.892017          18.660885           8.9591293


next up previous contents
Next: RANDMULTI Generate Multinomial-distributed Random Up: Random Number Generation Previous: RANDF Generate F-Distributed Random   Contents
Samit K. Basu 2005-03-16