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# Chi Distribution Random Number Generator

The chi-distribution with *k* degrees of freedom, χ_{ k} , is the distribution of the square root of the sum of the squares of *k* standard normal random variables. For example, if *R*, *S*, and *T* are drawn from a normal distribution with a mean of 0 and variance of 1, then

sqrt(*R*² + *S*² + *T*²)

has a χ_{3} distribution. You can use the calculator below to generate random χ_{ k} variables.

The PDF of the chi distribution is given by the equation

The theoretical mean, median, mode, variance, and skewness of the chi distribution depend upon

*k*. The equations are more complicated than for the chi-squared distribution.

The median of the chi-distribution does not have a closed form, however, it can be closely approximated with the function below:

k = 1: median = 0.674

k = 2: median = 1.177

k = 3: median = 1.5838

k > 3: median = 0.886

*k*

^{0.5336}

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