## truncated Gumbels

Posted in Books, Kids, pictures, Statistics with tags , , , , , , , on April 6, 2018 by xi'an

As I had to wake up pretty early on Easter morning to give my daughter a ride, while waiting I came upon this calculus question on X validated of computing the conditional expectation of a Gumbel variate, conditional on its drifted version being larger than another independent Gumbel variate with the same location-scale parameters. (Just reminding readers that a Gumbel G(0,1) variate is a double log-uniform, i.e., can be generated as X=-log(-log(U)).) And found after a few minutes (and a call to Wolfram Alpha integrator) that

$\mathbb{E}[\epsilon_1|\epsilon_1+c>\epsilon_0]=\gamma+\log(1+e^{-c})$

which is simple enough to make me wonder if there is a simpler derivation than the call to the exponential integral Ei(x) function. (And easy to check by simulation.)

Incidentally, I discovered that Emil Gumbel had applied statistical analysis to the study of four years of political murders in the Weimar Republic, demonstrating the huge bias of the local justice towards right-wing murders. When he signed the urgent call [for the union of the socialist and communist parties] against fascism in 1932, he got expelled from his professor position in Heidelberg and emigrated to France, which he had to leave again for the USA on the Nazi invasion in 1940. Where he became a professor at Columbia.

## Philosophenweg (im Toronto)

Posted in pictures, Running, Travel with tags , , , , , , , on November 2, 2013 by xi'an

Apart from walking the philosopher’s way (or path) in Toronto, after Heidelberg and Kyoto, I had a very enjoyable time (if not weather) for my very first time visit to the University of Toronto, from discussions with several friends of old, to a well-attended seminar, to a grilled octopus lunch in an faculty club and a (French) dinner au Paradis, to seeing a variety of costumes parading the streets for Halloween, with different varieties at six p.m. and two a.m., and to a discovery run in the early and windy Friday morning in the streets of Toronto.

## New arXiv papers

Posted in Statistics, Travel, University life with tags , , , , on June 16, 2010 by xi'an

Some recent arXiv papers I will not have time to comment:

## Sonnenaufgang über dem Neckar

Posted in pictures, Travel with tags , , on April 16, 2010 by xi'an

A picture of this morning sunrise over the Neckar river in Heidelberg.

## Seminars in Heidelberg

Posted in Statistics, Travel with tags , , on April 12, 2010 by xi'an

On Thursday and Friday, I am giving two seminars in Heidelberg. One on computational approches to computing the Bayes factor and one on ABC methods (both talks being at 14:15 in the Mathematics Center).