Publications by arthur charpentier
MAT8886 elliptically contoured distributions
Last week, we’ve introduced the concept of exchangeable variables, i.e. satisfying for any matrix , i.e. is a permutation matrix: belongs to the orthogonal group, , and with elements in . It is possible to extend that family, considering all matrices in the orthogonal group, i.e. for all . Since orthogonal matrices can be see...
2934 sym R (469 sym/1 pcs) 88 img
MAT8886 the Dirichlet distribution
In the course, still introducing some concept of dependent distributions, we will talk about the Dirichlet distribution (which is a distribution over the simplex of ). Let denote the Gamma distribution with density (on ) Let denote independent random variables, with . Then where has a Dirichlet distribution with parameter . Note that has a...
1451 sym R (204 sym/1 pcs) 74 img 1 tbl
MAT8886 reducing dimension using factors
First, let us recall a standard result from linear algebra: “real symmetric matrices are diagonalizable by orthogonal matrices“. Thus, any variance-covariance matrix can be written since a variance-covariance matrix is also definite positive. In the context of Gaussian random vectors (or more generally elliptical distributio...
2011 sym R (800 sym/3 pcs) 40 img 1 tbl
Visualization in regression analysis
Visualization is a key to success in regression analysis. This is one of the (many) reasons I am also suspicious when I read an article with a quantitative (econometric) analysis without any graph. Consider for instance the following dataset, obtained from http://data.worldbank.org/, with, for each country, the GDP per capita (in ...
1630 sym R (4451 sym/8 pcs) 24 img
Do we appreciate sunbathing in Spring ?
We are currently experiencing an extremely hot month in Montréal (and more generally in North America). Looking at people having a beer, and starting the first barbecue of the year, I was wondering: if we asked people if global warming was a good or a bad thing, what do you think they will answer ? Wearing a T-shirt in Montréal in March is nice...
3969 sym R (2433 sym/13 pcs) 10 img
Ruin probability and infinite time
A couple of weeks ago, I had a discussion with a practitioner, working in some financial company, about ruin, and infinite time. And it remind me a weird result. Well, not a weird result, but a result I found disturbing, at first, when I was a student (that I rediscovered with the eyes of someone dealing with computational issues, seeing here a d...
3676 sym R (594 sym/4 pcs) 120 img
Maths can be cool (to impress your kids)
Just imagine that your kids need some help, to prepare fishes for April 1st, like Her: “please, Daddy, help us to draw some fishes“ Me: “Sure, Daddy is a champion, actually, I do that everyday at work: drawing fishes – and more generally nice stuff – is exactly Daddy’s job“. OK, no need to talk neither about Talbot’s curves, ell...
924 sym R (348 sym/2 pcs) 8 img 1 tbl
Sunday evening, stupid games…
This evening, while I was about to wash the dishes, I heard my elders starting a game (call them Him and Her) Him: “I have picked – in my head – a number, lower than 50. Try to guess…“ Her: “No way, too difficult…“ Him: “You can try five different numbers…“ Her: “.,. um … No, no way…“ Me: “Wait… e...
3344 sym R (771 sym/5 pcs) 6 img
Playing with fire (or water)
A few days ago, http://www.futilitycloset.com/ published a short post based on the fourth problem of the 1987 Canadian Mathematical Olympiad (from on a problem from the 6th All Soviet Union Mathematical Competition in Voronezh, 1966). The problem is simple (as always). It is about water pistol duels (with an odd number of players) The answer i...
1601 sym R (485 sym/3 pcs) 6 img
Where hiding if you don’t want to get wet ?
Following the previous post, two additional remarks. Following a comment by @cosi, I have investigated quickly a binomial fit to the distribution of the number of people not getting wet, with a fixed number of players on the field. It looks like it should be a binomial distribution with a fixed probability (2/3) and with size parameter affine in ...
3699 sym R (2329 sym/8 pcs) 38 img 7 tbl