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Statistics[Distributions]

  

Rayleigh

  

Rayleigh distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Rayleigh(b)

RayleighDistribution(b)

Parameters

b

-

scale parameter

Description

• 

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

ft&equals;piecewiset<0&comma;0&comma;t&ExponentialE;12t2b2b2

  

subject to the following conditions:

0<b

• 

The Rayleigh variate with scale parameter b is equivalent to the Weibull variate with scale parameter b and shape parameter 2:  Rayleigh(b) ~ Weibull(b,2).

• 

The Rayleigh variate with scale parameter 1 is equivalent to a ChiSquare variate with degrees of freedom 2:  Rayleigh(1) ~ ChiSquare(2).

• 

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

Examples

withStatistics&colon;

XRandomVariableRayleighb&colon;

PDFX&comma;u

&lcub;0u<0u&ExponentialE;12u2b2b2otherwise

(1)

PDFX&comma;0.5

0.5&ExponentialE;0.1250000000b2b2

(2)

MeanX

12b2&pi;

(3)

VarianceX

212&pi;b2

(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]