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.








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