The probability density function and cumulative distribution functions for Student's -distribution are
given by

(1) | |||

(2) |

The Mean is 0, so the Moments are

(3) | |||

(4) | |||

(5) | |||

(6) |

The Mean, Variance, Skewness, and Kurtosis are

(7) | |||

(8) | |||

(9) | |||

(10) |

Letting

(11) |

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1999-05-26