The probability density function and cumulative distribution function are
(1) | |||
(2) |
(3) | |||
(4) | |||
(5) | |||
(6) |
where is the Mean, the Variance, the Skewness, and the Kurtosis. For , the distribution is a Half-Normal Distribution with . For , it is a Rayleigh Distribution with .
See also Chi-Squared Distribution, Half-Normal Distribution, Rayleigh Distribution