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 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.