Random Number Generator - F Distribution



The F distribution is commonly used for ANOVA (analysis of variance), to test whether the variances of two or more populations are equal.  For every F deviate, there are two degrees of freedom, one in the numerator and one in the denominator.  It is the ratio of the dispersions of the two Chi-Square distributions.  As both of the degree of freedom increase, the percentile value is approaching to one.  F is also used in tests of “explained variance” and is referred to as the variance ration – Explained variance/Unexplained variance. 

The following example shows input and output from 3 simulations.  Each has the degrees of freedom of (2,12), (30,15), and (60,120) respectively.  All three simulations have 10,000 iterations and alpha of 1% (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 .  Many things happened as the degree of freedom becoming larger from simulation 1 to 3:  the percentile value also approaching to 1; skew level decreases (the distribution approaches to normal); mean is approaching to 1 (mean(F) = df2/(df2-2)); the standard deviation decreases.

The following three charts show as degree of freedom increases, the distribution approaches to normal.

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