Random Number Generator - Chi-Square Distribution



The most common use of the chi-square distribution is to test the difference between proportions.  It has a positive skew.  The skew decreases when degree of freedom increases as the distribution approaches normal.  The mean of a chi-square distribution is its degree of freedom. 

The following example shows input and output from 3 simulations.  Each has the degree of freedom of 10, 50, and 500, respectively.  All three simulations have 10,000 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 .  Each of the 3 means are very closed to its corrsponding degree of freedom.

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.