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Statistics[Distributions][Laplace] - Laplace distribution

Calling Sequence

Laplace(a, b)

LaplaceDistribution(a, b)

Parameters

a

-

location parameter

b

-

scale parameter

Description

• 

The Laplace distribution is a continuous probability distribution with probability density function given by:

ft=12ⅇtabb

  

subject to the following conditions:

a::real&comma;0<b

• 

The Laplace variate with location parameter 0 and scale parameter b is related to two independent Exponential variates E1 and E2 by Laplace(0,b) ~ E1 - E2.

• 

Note that the Laplace command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

X:=RandomVariableLaplacea&comma;b&colon;

PDFX&comma;u

12&ExponentialE;u&plus;abb

(1)

PDFX&comma;0.5

0.5000000000&ExponentialE;1.0.5&plus;abb

(2)

MeanX

a

(3)

VarianceX

2b2

(4)

See Also

Statistics, Statistics[Distributions], Statistics[RandomVariable]

References

  

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions 3rd ed. Hoboken: Wiley, 2000.

  

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.


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