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Statistics[Distributions][Power] - power distribution
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Calling Sequence
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Power(b, c)
PowerDistribution(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 power 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 power variate with scale parameter 1 and shape parameter c is related to the Beta variate with first scale parameter c and second scale parameter 1 by Power(1,c) ~ Beta(c,1).
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The power variate with scale parameter b and shape parameter 1 is equivalent to the Uniform variate with lower bound parameter 0 and upper bound parameter b: Power(b,1) ~ Uniform(0,b).
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Note that the Power 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)/b^c, u <= b], [0, otherwise])](/support/helpjp/helpview.aspx?si=4659/file06597/math113.png)
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![PIECEWISE([c*.5^(-1.+c)/b^c, .5 <= b], [0., otherwise])](/support/helpjp/helpview.aspx?si=4659/file06597/math120.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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