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Statistics[Distributions][Weibull] - Weibull distribution
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Calling Sequence
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Weibull(b, c)
WeibullDistribution(b, c)
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Parameters
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b
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scale parameter
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c
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shape parameter
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Description
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The Weibull 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 Weibull variate is related to the standard Weibull variate by Weibull(b,c) ~ b*Weibull(1,c).
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The Weibull variate with scale parameter b and shape parameter 1 is equivalent to the Exponential variate with scale parameter b: Weibull(b,1) ~ Exponential(b).
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The Weibull variate with scale parameter b and shape parameter 2 is equivalent to the Rayleigh variate: Weibull(b,2) ~ Rayleigh(b).
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Note that the Weibull 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], [c*u^(c-1)*exp(-(u/b)^c)/b^c, otherwise])](/support/helpjp/helpview.aspx?si=3856/file06604/math111.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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