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Statistics[Distributions]

  

InverseGaussian

  

inverse Gaussian (Wald) distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

InverseGaussian(mu, lambda)

InverseGaussianDistribution(mu, lambda)

Parameters

mu

-

distribution mean

lambda

-

scale parameter

Description

• 

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

ft=0t<02λπt3&ExponentialE;λtμ22μ2t2otherwise

  

subject to the following conditions:

0<μ,0<λ

• 

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

Examples

withStatistics&colon;

XRandomVariableInverseGaussian&mu;&comma;&lambda;&colon;

PDFX&comma;u

0u<02λπu3&ExponentialE;λuμ22μ2u2otherwise

(1)

PDFX&comma;0.5

1.128379166λ&ExponentialE;1.000000000λ0.51.μ2μ2

(2)

MeanX

μ

(3)

VarianceX

μ3λ

(4)

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.

See Also

Statistics

Statistics[Distributions]

Statistics[RandomVariable]