“Fisher's z-Distribution”的概念、定义、习题解题方法及翻译-数学辞典

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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