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 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.