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

单词

Laplace Distribution

释义

Laplace Distribution

Also called the Double Exponential Distribution. It is the distribution of differences between two independentvariates with identical Exponential Distributions (Abramowitz and Stegun 1972,p. 930).

			(1)
			(2)

The Moments about the Mean

are related to the Moments about 0 by

(3)

where

is a Binomial Coefficient, so


			(4)

where

is the Floor Function and

is the GammaFunction.

The Moments can also be computed using the Characteristic Function,

(5)

Using the Fourier Transform of the Exponential Function

(6)

gives

(7)

The Moments are therefore

(8)

The Mean, Variance, Skewness, and Kurtosis are

			(9)
			(10)
			(11)
			(12)

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.

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