If a random variable has a chi-squared distribution with degrees of freedom () and a random variable has a chi-squared distribution with degrees of freedom (), and and are independent, then
(1)
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is distributed as Snedecor's -distribution with and degrees of freedom
(2)
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for . The raw moments are
(3)
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(4)
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(5)
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(6)
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so the first few central moments are given by
(7)
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(8)
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(9)
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and the mean, variance, skewness, and kurtosis excess are
(10)
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(11)
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(12)
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(13)
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The characteristic function can be computed, but it is rather messy and involves the generalized hypergeometric function .
Letting
(14)
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gives a beta distribution (Beyer 1987, p. 536).