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单词 Weibull Distribution
释义

Weibull Distribution

The Weibull distribution is given by

(1)
(2)

for (Mathematica Statistics`ContinuousDistributions`WeibullDistribution[a,b], Wolfram Research, Champaign, IL).The Mean, Variance, Skewness, and Kurtosis of this distribution are
(3)
(4)
 
 (5)
(6)

where is the Gamma Function and

(7)


A slightly different form of the distribution is

(8)
(9)

(Mendenhall and Sincich 1995). The Mean and Variance for this form are
(10)
(11)


The Weibull distribution gives the distribution of lifetimes of objects. It was originally proposed to quantify fatiguedata, but it is also used in analysis of systems involving a ``weakest link.''

See also Fisher-Tippett Distribution


References

Mendenhall, W. and Sincich, T. Statistics for Engineering and the Sciences, 4th ed. Englewood Cliffs, NJ: Prentice Hall, 1995.

Spiegel, M. R. Theory and Problems of Probability and Statistics. New York: McGraw-Hill, p. 119, 1992.


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