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单词 Fisher's z-Distribution
释义

Fisher's z-Distribution


(1)

(Kenney and Keeping 1951). This general distribution 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
(2)

Then let
(3)

so that is a ratio of Chi-Squared variates
(4)

which makes it a ratio of Gamma Distribution variates, which is itself a Beta Prime Distribution variate,
(5)

giving
(6)

The Mean is
(7)

and the Mode is
(8)

See also Beta Distribution, Beta Prime Distribution, Chi-Squared Distribution, Gamma Distribution,Normal Distribution, Student's t-Distribution


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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更新时间:2024/11/15 1:59:08