威布爾如何得出三個參數的威布爾分佈?


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[1]: https://i.stack.imgur.com/zAuui.png

魏布爾或任何其他數學家如何得出上述表達式?我看到了1951年的論文,但我不清楚。1939年,他出版了一本書,名為《材料強度的統計理論》,目前我正在尋找這本書。同時,任何人都可以向我解釋。

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The paper "Strength of materials and the Weibull distribution" by Eric S. Lindquist in Probabilistic Engineering Mechanics 9 (1994) 191-194 probably has what you want. I found several online copies with a "weibull's original paper" google search, but they might be behind institutional paywalls.

Weibull's 1939 paper "A statistical theory of the strength of materials" seems to have appeared in what WorldCat says was this journal:

Ingeniörsvetenskapsakademiens handlingar = Proceedings / Royal Swedish Academy of engineering sciences the Royal Swedish Institute for scientific engineering research = formerly: Proceedings / the Royal Swedish Institute for engineering research

in volume 151, pp.1-45. I have not found any on-line copies of this paper. WorldCat lists libraries on 3 continents with this journal; the nearset to me is about 100 km away from where I live, the 6-th nearest in another country.

Two of the 3 parameters, $\gamma$ and $\eta$ (this is me talking, not Lindquist) are location and scale parameters, more or less inevitable in any technological application. The third, $\beta$ is the interesting one.