## an elegant result on exponential spacings

Posted in Statistics with tags , , , , , , , , , , , , , on April 19, 2017 by xi'an

A question on X validated I spotted in the train back from Lyon got me desperately seeking a reference in Devroye’s Generation Bible despite the abyssal wireless and a group of screeching urchins a few seats away from me… The question is about why

$\sum_{i=1}^{n}(Y_i - Y_{(1)}) \sim \text{Gamma}(n-1, 1)$

when the Y’s are standard exponentials. Since this reminded me immediately of exponential spacings, thanks to our Devroye fan-club reading group in Warwick,  I tried to download Devroye’s Chapter V and managed after a few aborts (and a significant increase in decibels from the family corner). The result by Sukhatme (1937) is in plain sight as Theorem 2.3 and is quite elegant as it relies on the fact that

$\sum_{i=1}^n y_i=\sum_{j=1}^n (n-j+1)(y_{(j)}-y_{(j-1)})=\sum_{j=2}^n (y_{(j)}-y_{(1)})$

hence sums up as a mere linear change of variables! (Pandurang Vasudeo Sukhatme (1911–1997) was an Indian statistician who worked on human nutrition and got the Guy Medal of the RSS in 1963.)

## ODOF, not Hodor [statlearn 2017]

Posted in Books, Kids, pictures, Statistics, University life with tags , , , , , , , , on April 15, 2017 by xi'an

## Fourvière [jatp]

Posted in Mountains, pictures, Running, Travel with tags , , , , , , on April 13, 2017 by xi'an

## Saône, sunrise #2 [jatp]

Posted in pictures, Running, Travel, University life with tags , , , , , , , , , , on April 10, 2017 by xi'an

## Saône, sunrise [jatp]

Posted in pictures, Running, Travel, University life, Wines with tags , , , , , , , , on April 8, 2017 by xi'an

## Statlearn17, Lyon

Posted in Kids, pictures, R, Statistics, Travel, University life with tags , , , , , , , , , , on April 6, 2017 by xi'an

Today and tomorrow, I am attending the Statlearn17 conference in Lyon, France. Which is a workshop with one-hour talks on statistics and machine learning. And which makes for the second workshop on machine learning in two weeks! Yesterday there were two tutorials in R, but I only took the train to Lyon this morning: it will be a pleasant opportunity to run tomorrow through a city I have not truly ever visited, if X’ed so many times driving to the Alps. Interestingly, the trip started in Paris with me sitting in the train next to another speaker at the conference, despite having switched seat and carriage with another passenger! Speaker whom I did not know beforehand and could only identify him by his running R codes at 300km/h.

## la Saintélyon

Posted in Mountains, pictures, Running with tags , , , , on December 8, 2013 by xi'an

At this very moment, the competitors of the saintélyon ultratrail are starting from Saint-Étienne for a nocturnal trail run of 75km to Lyon. (Hence the name.) This classic race takes place in the Monts du Lyonnais between the two cities and it is usually very cold, with ice and snow most of the way. The total differential is 1800m D+ / 2100m D-, with a record time of 5:16 last year (and an overall record time of 4:19!)… At least two of my running friends & colleagues, Julyan and Marc, are competing this year, so all the best to them (and the 12 000 other runners) for this ultratrail!

And a few hours later, congratulations to both of them for their finisher status! Bravo!