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.