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Date: 16-2-2021
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Date: 11-3-2021
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Date: 7-4-2021
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Fischer's -distribution is the general distribution defined by
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(1) |
(Kenney and Keeping 1951) which includes the chi-squared distribution and Student's t-distribution as special cases.
Let and
be independent unbiased estimators of the variance of a normally distributed variate. Define
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(2) |
Then let
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(3) |
so that is a ratio of chi-squared variates
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(4) |
which makes it a ratio of gamma distribution variates, which is itself a beta prime distribution variate,
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(5) |
giving
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(6) |
The mean is
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(7) |
and the mode is
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(8) |
REFERENCES:
Kenney, J. F. and Keeping, E. S. Mathematics of Statistics, Pt. 2, 2nd ed. Princeton, NJ: Van Nostrand, pp. 180-181, 1951.
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