3 ms·
A lady at work was talking about this years ago, and I had a look. It's pretty interesting, because it focuses on the opposite of what we're normally introduced
by lordnacho 3y ago
A lady at work was talking about this years ago, and I had a look. It's pretty interesting, because it focuses on the opposite of what we're normally introduced to in stats classes, that being measures of central tendency.
Somehow it isn't often talked about. For instance, if you have some gaussian and you sample from it a small number of times, what is the distribution of the largest value?
- sudosysgen 3y agoYou would use one of the Generalized Extreme Value distributions. One of those, the Gumbel distribution, is actually commonly used in machine learning to sample from a softmax in a differentiable manner (by reparametrization), and should work for the maximum of normals (it's definitely one of the three). You may be interested in this theorem : https://en.m.wikipedia.org/wiki/Fisher%E2%80%93Tippett%E2%80%93Gnedenko_theorem https://en.m.wikipedia.org/wiki/Fisher%E2%80%93Tippett%E2%80...
- klysm 3y agoVery interesting second question! I wonder what distribution it follows as a function of sample quantity
- bo1024 3y agoIn some formats, the question is easy. If the CDF is F(x), then the CDF of the maximum of n independent draws is G(x) = F(x)^n. This is because the probability that the max is less than x is the product of the probabilities that each is less than x.