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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