Random Number Generator - Gamma Distribution



The Gamma distribution is most often used to describe the distribution of the amount of time until the nth occurrence of an event in a Poisson process.  For example, customer service or machine repair.  The Gamma distribution is related to many other distributions.  For example, when a Gamma distribution has an alpha of 1, Gamma(1, b), it becomes an Exponential distribution with scale parameter of b, Expo(b).  And a Chi-Square distribution with k df is the same as the Gamma(k/2, 2) distribution.

The following example shows input and output from 3 simulations.  Gamma(1,1), Gamma(2,1), and Gamma(3,1).  All three simulations have 50,000 iterations and alpha of 5% (for 1 tail test).

The output shows the estimate of skew level, mean, stand deviation, maximum value, minimum value, lower confidence interval, and upper confidence interval from each of the 3 simulations.  The skew levels decreases as the scale parameter, b, increases.  All three means approximate the product of a and b.  

The following shows the charts generated from the 3 simulations.

Complete program (with open source codes) available in Package Set 2 and the Combo Package.