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Statistics[Distributions]

  

Weibull

  

Weibull distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Weibull(b, c)

WeibullDistribution(b, c)

Parameters

b

-

scale parameter

c

-

shape parameter

Description

• 

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

ft&equals;piecewiset<0&comma;0&comma;ctc1&ExponentialE;tbcbc

  

subject to the following conditions:

0<b&comma;0<c

• 

The Weibull variate is related to the standard Weibull variate by Weibull(b,c) ~ b*Weibull(1,c).

• 

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).

• 

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

• 

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

Examples

withStatistics&colon;

XRandomVariableWeibullb&comma;c&colon;

PDFX&comma;u

&lcub;0u<0cuc1&ExponentialE;ubcbcotherwise

(1)

PDFX&comma;0.5

c0.51.&plus;c&ExponentialE;1.0.5bcbc

(2)

MeanX

b&Gamma;1&plus;cc

(3)

VarianceX

b2&Gamma;c&plus;2c&Gamma;1&plus;cc2

(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]

 


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