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 ¡V 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.