Weibull Distribution
المؤلف:
Johnson, N.; Kotz, S.; and Balakrishnan, N
المصدر:
Continuous Univariate Distributions, Vol. 2, 2nd ed. New York: Wiley, 1995.
الجزء والصفحة:
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16-4-2021
1807
Weibull Distribution
The Weibull distribution is given by
for 
, and is implemented in the Wolfram Language as WeibullDistribution[alpha, beta]. The raw moments of the distribution are
and the mean, variance, skewness, and kurtosis excess of are
where 
is the gamma function and
 |
(11)
|
A slightly different form of the distribution is defined by
(Mendenhall and Sincich 1995). This has raw moments
so the mean and variance for this form are
The Weibull distribution gives the distribution of lifetimes of objects. It was originally proposed to quantify fatigue data, but it is also used in analysis of systems involving a "weakest link."
REFERENCES:
Johnson, N.; Kotz, S.; and Balakrishnan, N. Continuous Univariate Distributions, Vol. 2, 2nd ed. New York: Wiley, 1995.
Kobayashi, A. (Ed.). Handbook on Experimental Mechanics. New York: VCH/SEM, 1993.
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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