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Statistics[Distributions][Power] - power distribution

Calling Sequence

Power(b, c)

PowerDistribution(b, c)

Parameters

b

-

scale parameter

c

-

shape parameter

Description

• 

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

ft&equals;piecewiset<0&comma;0&comma;tb&comma;ctc1bc&comma;0

  

subject to the following conditions:

0<b&comma;0<c

• 

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).

• 

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).

• 

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

Examples

withStatistics&colon;

X:=RandomVariablePowerb&comma;c&colon;

PDFX&comma;u

&lcub;0u<0cuc1bcub0otherwise

(1)

PDFX&comma;0.5

&lcub;c0.51.&plus;cbc0.5b0.otherwise

(2)

MeanX

bc1&plus;c

(3)

VarianceX

b2cc&plus;21&plus;c2

(4)

See Also

Statistics, Statistics[Distributions], Statistics[RandomVariable]

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.


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