Talk:Stretched exponential function

Double exponential distribution in Figure 1
I believe that the author meant the Gumbel distribution. Any comments?

TomyDuby (talk) 04:03, 7 January 2010 (UTC)

I believe you are right. Gumbel distribution is also termed double exponential. But it is sorts of trick, since Laplace distribution bears the name too.BrennoBarbosa (talk) 23:41, 9 February 2014 (UTC)

Generalized Gamma Distribution
Generally, the stretched exponential function is associated with a life time distribution (reliability or survival analysis). For example, one may be interested in some decay time for fluorescence etc.. In this case, we can regard such "probability density function" as a particular case of the Generalized gamma distribution. I'm far from being a expert in any of this issue, but I think it is worth mentioning somehow.BrennoBarbosa (talk) 23:35, 9 February 2014 (UTC)

Area under the curve
Why does the article say that the area under the curve is the mean? Shouldn't the area under the curve be the inverse normalization constant, and the mean be
 * $$\langle\tau\rangle \equiv \frac{1}{{\tau_K \over \beta } \Gamma \left({1 \over \beta }\right)} \int_0^\infty dt\, t\,e^{-(t/\tau_K)^\beta} = \frac{\tau_K \Gamma\left(\frac{2}{\beta}\right)}{\Gamma\left(\frac{1}{\beta}\right)}?$$

Sprlzrd (talk) 23:26, 7 April 2020 (UTC)

Probability distribution function
The probability distribution function ρ(u) as given in the article is certainly not correct as it does not peak near 1 for β near 1. If the final part, uβk, is replace by u-βk, it's better but still not quite right. The mistake originates in the original article https://doi.org/10.1063%2F1.440530 Eq. (24) to (25).

Eq. (34) from https://doi.org/10.1016%2Fj.chemphys.2005.04.006 is better but not quite in the right form (written as function of rate rather than time). May change it myself later IwptsA (talk) 17:15, 2 May 2023 (UTC)