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.