Chi-Square Distribution

The chi-square distribution is a widely used probability distribution in statistics. It has the property that the mean of the distribution is equal to the degrees of freedom and the variance is twice the number of degrees of freedom. As the degrees of freedom increases, the chi-square distribution approaches a normal distribution.

There are many uses of the chi-square statistic. The most widely use is in determining if distributions of categorical variables differ from one another.

The probability density function of the chi-square distribution is:

where k is a parameter corresponding to the degrees of freedom and Gamma is the Gamma function defined by...

The figure above was generated using Matlab.