The probability density function and cumulative distribution function are

(1) | |||

(2) |

where is the Regularized Gamma Function.

(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 .

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1999-05-26