Hi Pierre, My answers to your questions are below... On 1/14/19, Pierre Haessig <pierre.haessig@crans.org> wrote:
Hello,
I just submitted a small PR to clarify the docstring of exponweib distribution in scipy.stats (https://github.com/scipy/scipy/pull/9679).
However, in the process, I got a bit confused with weibull_min and weibull_max. It seems that up to Scipy 0.19, it was specified as an alias to Frechet left distribution (https://docs.scipy.org/doc/scipy-0.19.0/reference/generated/scipy.stats.weib...). However this is not mentioned anymore since 1.0.
For a long time, weibull_min and weibull_max were aliases of frechet_l and frechet_r. The problem was that the implementations in frechet_l and frechet_r were not what anyone calls the Fréchet distribution these days. They were, in fact, what are almost universally called the Weibull distribution. So in SciPy 1.0.0, those implementations were moved to the weibull_min and weibull_max names, and the names frechet_r and frechet_l were deprecated (see https://github.com/scipy/scipy/pull/7838 for the details of the changes). The names frechet_l and frechet_r still exist, but if you use any of their methods, you will get a deprecation warning. (Unfortunately, it looks like I neglected make a note of this deprecation in the 1.0.0 release notes.) The distribution that is generally known as *the* Fréchet distribution is also known as the inverse Weibull distribution (see, for example, https://en.wikipedia.org/wiki/Fr%C3%A9chet_distribution). It is implemented in SciPy as scipy.stats.invweibull.
Also, it seems that weibull_min corresponds to the usual Weibull distribution, but its docstring doesn't say it explicitly. Also, I find no references on the web for those Weibull min/max. Would it be appropriate, in the long term, to simply have a Weibull distribution?
The extreme value distributions arise as the limiting distribution of taking the exteme value (i.e. maximum or minimum) of a large number of samples from some underlying distribution. For a certain class of underlying distributions, if you take the maximum, in the (appropriately renormalized) limit you get the distribution that SciPy calls weibull_max, and if you take the minimum, you get weibull_min. (These distributions are related: if F(x, c) is the CDF of weibull_min with shape parameter c, then the CDF of weibull_max is 1 - F(-x, c).) The issue, then, is which one should be considered the "usual" Weibull distribution? The answer is not obvious. For example, the distribution described in the wikipedia article on the Weibull distribution (https://en.wikipedia.org/wiki/Weibull_distribution) corresponds to weibull_min. This is also the distribution from which numpy.random.weibull draws samples. On the other hand, in the book "An Introduction to Statistical Modeling of Extreme Values" by Stuart Coles, and in the book "Modelling Extremal Events" by Embrechts, Klüppelberg and Mikosch (two widely used texts on extreme value theory), the distribution that is called the Weibull distribution corresponds to SciPy's weibull_max. So I think we are better off *not* picking one to be called the "usual" Weibull distribution. The current names accurately describe the basis of the two flavors of the distribution. However, we should improve the documentation to include this information about the min/max distinction in their docstrings. We should do the same for gumbel_l and gumbel_r. I'd be happy to make this change, but I probably won't get to it in the near future, so I'd be even happier if someone created a pull request that added this information to the docstrings of weibull_min and weibull_max. Similar updates for gumbel_l and gumber_r could be made at the same time or in a separate pull request. (The original implementations of these extreme value distributions dates back to before my involvement with SciPy, so I can't say why the Weibull distribution used the suffixes _min and _max while the other distributions with two conventions used _l and _r, and I don't know why we don't have the two versions for the inverse Weibull--a.k.a. Fréchet-- distribution.) Warren