Random Number Generator - Beta Distribution



The Beta distribution can be used in the absence of data.  Possible applications are estimate the proportion of defective items in a shipment or time to complete a task.  The Beta distribution has two shape parameters, a1 and a2.  When the two parameters are equal, the distribution is symmetrical.  For example, when both a1 and a2 are equal to one, the distribution becomes uniform.  If a1 is less than a2, the distribution is skewed to the left.  And if a1 is greater than a2, the distribution is skewed to the right.

The following example shows input and output from 3 simulations with Beta(9,2), Beta(9,9), and Beta(2,9).  All three simulations have 50,000 iterations and alpha of 5% (for 1 tail test).

The output shows the estimate of skewness, mean, stand deviation, maximum value, minimum value, lower confidence interval, and upper confidence interval from each of the 3 simulations.  The result from the second iteration shows that skew is zero and the mean (0.50) lays between the lower and upper confidence interval (0.31 and 0.69).  This indicates that the distribution is symmetric as shown on chart 2.  The first chart and the third chart confirm with the analysis in our introductory paragraph about how the skew level behaviors given a1 is greater than a2 and vice versa.

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.