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

单词

Exponential Distribution

释义

Exponential Distribution

Given a Poisson Distribution with rate of change , the distribution of waiting times between successivechanges (with ) is

which is normalized since


			(3)

This is the only Memoryless Random Distribution. Define the Meanwaiting time between successive changes as

. Then

(4)

The Moment-Generating Function is

The Skewness and Kurtosis are given by

			(13)
			(14)

The Mean and Variance can also be computed directly

(15)

Use the integral

(16)

to obtain

Now, to find

(18)

use the integral

(19)


			(20)

giving

If a generalized exponential probability function is defined by

(23)

then the Characteristic Function is

(24)

and the Mean, Variance, Skewness, and Kurtosis are

See also Double Exponential Distribution

References

Balakrishnan, N. and Basu, A. P. The Exponential Distribution: Theory, Methods, and Applications. New York: Gordon and Breach, 1996.

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 534-535, 1987.

Spiegel, M. R. Theory and Problems of Probability and Statistics. New York: McGraw-Hill, p. 119, 1992.

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