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Statistics[Distributions][Rayleigh] - Rayleigh distribution
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Calling Sequence
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Rayleigh(b)
RayleighDistribution(b)
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Description
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The Rayleigh distribution is a continuous probability distribution with probability density function given by:
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subject to the following conditions:
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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).
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The Rayleigh variate with scale parameter 1 is equivalent to a ChiSquare variate with degrees of freedom 2: Rayleigh(1) ~ ChiSquare(2).
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Note that the Rayleigh command is inert and should be used in combination with the RandomVariable command.
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Examples
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![PIECEWISE([0, u < 0], [u*exp(-(1/2)*u^2/b^2)/b^2, otherwise])](/support/helpjp/helpview.aspx?si=4128/file06599/math97.png)
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References
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Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
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Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
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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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