“Probability Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Probability Function

释义

Probability Function

The probability density function (also called the Probability Density Function) of a continuous distribution isdefined as the derivative of the (cumulative) Distribution Function ,

(1)

(2)

A probability density function satisfies

(3)

and is constrained by the normalization condition,

(4)

Special cases are

			(5)
			(6)
			(7)

If and , then

(8)

Given the Moments of a distribution (, , and the Gamma Statistics), the asymptotic probability function is given by





	(9)

where

(10)

is the Normal Distribution, and

(11)

for

(with

Cumulants and

the Standard Deviation; Abramowitz and Stegun1972, p. 935).

See also Continuous Distribution, Cornish-Fisher Asymptotic Expansion, Discrete Distribution,Distribution Function, Joint Distribution Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Probability Functions.'' Ch. 26 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 925-964, 1972.

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