Number Generator - F Distribution
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
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).
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
Complete program (with open source
codes) available in Package Set 2 and the Combo Package.