I have published my paper on an equation that calculates the optimal lambda for a Weibull distribution. You can download the pdf at this link.
Why this is so interesting, is that the exponent of 10 came from a regression analysis of Box-Cox transformation lambas where the intercept solved to the percent of a weibull distribution that is less than the scale parameter (characteristic life value) and the slope of the line is 1.000. It is uncommon to have a slope of zero, but to also have the intercept value equal a value that related to the distribution makes this more than a cooincidence.
The work was performed using the @Risk add-in to excel and Minitab.
I have considered an effort to derive this relationship using by solving the first derivitive of the Log(skewness equation) set equal to zero. But it involves the derivitive of a Gamma Distribution, which is not a trivial. During a literature review, I have not yet found any published result matching my proposed equation, but I have found another case where a log of a Wiebull distribution solved to a similar result.
Prior postings on this topic
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