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

单词

Snedecor's F-Distribution

释义

Snedecor's F-Distribution

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)

is distributed as Snedecor's

-distribution with

and

degrees of freedom

(2)

for

. The Moments about 0 are

			(3)
			(4)
			(5)
			(6)

so the Moments about the Mean are given by

			(7)
			(8)
			(9)

where

(10)

and the Mean, Variance, Skewness, and Kurtosis are

			(11)
			(12)
			(13)

			(14)

where

(15)

Letting

(16)

gives a Beta Distribution.

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

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 536, 1987.

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