The probability density function (also called the Probability Density Function) of a continuous distribution is
defined as the derivative of the (cumulative) Distribution Function ,

(1) |

(2) |

A probability density function satisfies

(3) |

(4) |

(5) | |||

(6) | |||

(7) |

If and , then

(8) |

Given the Moments of a distribution (, , and the Gamma Statistics ), the asymptotic probability function is given by

(9) |

(10) |

(11) |

**References**

Abramowitz, M. and Stegun, C. A. (Eds.). ``Probability Functions.'' Ch. 26 in
*Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.*
New York: Dover, pp. 925-964, 1972.

© 1996-9

1999-05-26