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Statistics[Distributions]

  

Moyal

  

Moyal distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Moyal(mu, sigma)

MoyalDistribution(mu, sigma)

Parameters

mu

-

mode parameter

sigma

-

scale parameter

Description

• 

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

ft=2ⅇtμ2σⅇtμσ22πσ

  

subject to the following conditions:

μ::real,0<σ

• 

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

Examples

withStatistics&colon;

XRandomVariableMoyal&mu;&comma;&sigma;&colon;

PDFX&comma;u

122&ExponentialE;12u&mu;&sigma;12&ExponentialE;u&mu;&sigma;&pi;&sigma;

(1)

PDFX&comma;0.5

0.3989422802&ExponentialE;0.50000000000.51.&mu;&sigma;0.5000000000&ExponentialE;1.0.51.&mu;&sigma;&sigma;

(2)

MeanX

&sigma;&gamma;&plus;ln2&plus;&mu;

(3)

VarianceX

12&sigma;2&pi;2

(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]

 


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