From: W. Trevor King Date: Sun, 29 Jun 2008 22:10:54 +0000 (+0000) Subject: Importing NanoBlogger post "Gumbel/Fisher-Tippett distributions" X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=eee1b523d2be2ad9c59320533a28dd030b16f416;p=blog.git Importing NanoBlogger post "Gumbel/Fisher-Tippett distributions" --- diff --git a/posts/Gumbel/Fisher-Tippett_distributions.mdwn b/posts/Gumbel/Fisher-Tippett_distributions.mdwn new file mode 100644 index 0000000..000c7f2 --- /dev/null +++ b/posts/Gumbel/Fisher-Tippett_distributions.mdwn @@ -0,0 +1,20 @@ +[[!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]]