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+[[!meta  title="Gumbel/Fisher-Tippett distributions"]]
+[[!meta  date="2008-06-29 18:10:54"]]
+Aha, the probability of Bell-model unfolding under constant force-loading has a name!
+It is a [Fisher-Tippett distribution](http://en.wikipedia.org/wiki/Fisher-Tippett_distribution), of which the Gumbel distribution is a particular type.
+However, NIST refers to it as a [minimum Gumbel distribution](http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm).
+
+Hmm, hopefully I'm not just confusing myself looking at the standardized form, let me go double check...
+What is a [cumulative distribution function]() anyway?
+Ah, `CDF(x)` is just the probability that the variable will be `<= x`, so the probability distribution function is given by `PDF(x) = -d(CDF)/dx`.
+
+Alright, looks like my distribution is a bit different than the Fisher-Tippett because I need a non-unity a factor `a` in `PDF(x) = exp(-ax/b)*exp[-exp(x/b)]` with `z := exp(-x/b)`.
+Basically, I have a Fisher-Tippett distribution with a poorly scaled `x`, but I don't know how to rescale `x` until I've fit my distribution.
+So the search continues...
+
+The [Gompertz-Makeham Law](http://en.wikipedia.org/wiki/Gompertz-Makeham_law_of_mortality) law for exponentially increasing failure rate is what I want.
+But Wikipedia says this is the same as Fisher-Tippett with time inversion.
+
+There is a nice discussion of aging in general, but not much math [here](http://longevity-science.org/Failure-Models-2006.pdf).
+
+[[!tag  theory]]