A couple of weeks ago, Rafael asked me if I had something on the history of extreme value theory. Since I will get back to fundamental results about extremes in my course, I promised I will write down a short post on all that issue. To start from the beginning, in 1928, Ronald Fisher and … Continue reading Fisher-Tippett theorem with an historical perspective
Tomorrow, we will discuss Fisher-Tippett theorem. The idea is that there are only three possible limiting distributions for normalized versions of the maxima of i.i.d. samples . For bounded distribution, consider e.g. the uniform distribution on the unit interval, i.e. on the unit interval. Let and . Then, for all and , i.e. the limiting … Continue reading Fisher-Tippett theorem and limiting distribution for the maximum
Hearing “there is a 10% chance of rain today” or “the medical test has a positive predictive value of 75%” shows that the probabilities are now everywhere. A probability is a quantity that is difficult to grasp, but essential when trying to theorize and measure chance, or randomness. And if mathematical theory finally came very … Continue reading (A brief) history of randomness, and simulation techniques
Entendre « il y a 10% de chances de pluie aujourd’hui » ou « le test médical a une valeur prédictive positive de 75% » montre que les probabilités sont aujourd’hui partout[i]. Une probabilité est une grandeur difficile à appréhender, mais incontournable quand on cherche à théoriser et mesurer le hasard. Et si la théorie mathématique est finalement arrivée … Continue reading (Petite) histoire du hasard et de la simulation
This week, in the MAT8595 course, before proving Fisher-Tippett theorem, we will get back on the proof of the Central Limit Theorem, and the class of stable distribution (in Lévy’s sense). In order to illustrate the problem of heavy tails, on the behavior of the mean, consider a sequence of i.i.d. Gaussian random variables ‘s. On top, … Continue reading Central Limit Theorem
In a few days, I will participate to a panel discussion in Montréal, chaired by Marin Dacos, entitled “Minor forms of academic communication: revamping the relationship between science and society?“, at the World Social Science Forum. I do not have much expertise (compared with colleagues involved in the panel) even if I frequently observe the … Continue reading The role of blogging in academia
Last week, we had a discussion with some colleagues about the fact that – in order to prepare for the SOA exams – we did not have time (so far) to mention results on extreme values in our actuarial program. I did gave an introduction in my nonlife actuarial models class, but it was only … Continue reading How old is the oldest person you know?
A few months ago, I did publish a post (in French) following my reading of Leonard Mlodinow’s the Drunkard’s Walk. More precisely, I mentioned a paragraph that I found extremely informative But it looks like those gangsters were not only stealing money. They were also stealing ideas, here from a British statistician, manely Leonard Henry Caleb Tippett. Leonard Tippett is … Continue reading Bristish Statisticians and American Gangsters
For the first homework, there was a tricky question in problem 29, chapter 5. Here is the maximum of n random variables i.i.d. uniformly distributed on the unit interval . I gave a hint last week about the cumulative distribution function for the maximum, i.e. is equal to the probability that all are smaller than , Then, we … Continue reading “standardized” version of the maximum
In the paper on the heat wave in Paris (mentioned here) I discussed changes in the distribution of temperature (and autocorrelation of the time series). During the workshop on Statistical Methods for Meteorology and Climate Change today (here) I observed that it was still an important question: is climate change affecting only averages, or does … Continue reading More climate extremes, or simply global warming ?
I will start here a short post on extreme values, with some historical perspective. In a recent paper (in French), I mentioned the use of the Pareto distribution as a standard model for extremes, but if reinsurers have been using the Pareto distribution for a long time (see here e.g.), the oldest mathematical models when … Continue reading Some historical remarks on extreme values