Blog Archives

Benford law and lognormal distributions

March 28, 2013
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Benford law and lognormal distributions

Benford’s law is nowadays extremely popular (see e.g. http://en.wikipedia.org/…). It is usually claimed that, for a given set data set, changing units does not affect the distribution of the first digit. Thus, it should be related to scale invariant distributions. Heuristically, scale (or unit) invariance means that the density of the measure  (or probability function) should be proportional to . Thus, because densities integrate to 1, the proportionality coefficient has…

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Happy St Patrick’s Day

March 17, 2013
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Happy St Patrick’s Day

I love Saint Patrick’s Day for, at least, two reasons. The first one is that, on March 17th, you can play out loud The Pogues, the second one is that it’s the only day in the year when I really enjoy getting a Guiness in a pub. And Guiness is important in statistical science (I did mention a couple of hours ago – on this blog –  that beers were…

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Examen intra, régression logistique et de Poisson

March 12, 2013
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Examen intra, régression logistique et de Poisson

L’examen intra du cours ACT2040 aura lieu mercredi matin, de 9:00 à 12:00. Aucun document autorisé, sauf les calculatrices (modèle standard, cf plan de cours), et les téléphones seront formellement interdits. Il y aura 34 questions portant sur la première partie du cours (jusqu’à la fin des modèles de comptage, sections 1 à 5 des transparents). 15 questions porteront sur la base décrite dans un précédant billet, sur le nombre…

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Multiple (smoothed) regression and portfolio exposure

March 9, 2013
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Multiple (smoothed) regression and portfolio exposure

Wednesday, in class, we’ve seen how to visualize a multiple regression model (with two continuous explanatory variables). Here, the goal is to predict the average cost of an insurance claim, using some covariates, e.g. the age of the driver, and the age of the car (recall that losses here are liability losses). The prediction obtained from a (standard) generalized linear model, with a log-link > reg1=glm(cout~ageconducteur+agevehicule,data=base,family=Gamma(link="log")) The code to visualize…

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Comparing quantiles for two samples

March 8, 2013
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Comparing quantiles for two samples

Recently, for a research paper, I some samples, and I wanted to compare them. Not to compare they means (by construction, all of them were centered) but there dispersion. And not they variance, but more their quantiles. Consider the following boxplot type function, where everything here is quantile related (which is not the case for standard boxplot, see http://freakonometrics.hypotheses.org/4138, in French) > boxplotqbased=function(x){ + q=quantile(x[is.na(x)==FALSE],c(.05,.25,.5,.75,.95)) + plot(1,1,col="white",axes=FALSE,xlab="",ylab="", + xlim=range(X),ylim=c(1-.6,1+.6)) +…

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Job for life ? Bishop of Rome ?

February 26, 2013
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Job for life ? Bishop of Rome ?

The job of Bishop of Rome – i.e. the Pope – is considered to be a life-long commitment. I mean, it usually was. There have been 266 popes since 32 A.D. (according to http://oce.catholic.com/…): almost all popes have served until their death. But that does not mean that they were in the job for long… One can easily extract the data from the website, > L2=scan("http://oce.catholic.com/index.php?title=List_of_Popes",what="character") Read 4485 items >…

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Further readings on GLMs and ratemaking

February 21, 2013
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Further readings on GLMs and ratemaking

Some articles found in Actuarial journal, on ratemarking, Predictive Modeling—You Mean Actuarial Wizardry?, by Shane Barnes, http://casact.org/newsletter/… Predictive Modeling of Multi-Peril Homeowners Insurance  by Edward Frees, Glenn Meyers and David Cummings, http://variancejournal.org/issues/… see also Predictive Modeling of Multi-Peril Homewoners Insurance Predictive Modeling by Serhat Guven, http://casact.org/newsletter/… “Goodness of Fit” vs. “Goodness of Lift”, by Glenn Meyers and David Cummings, http://casact.org/newsletter/… Pure Premium Regression with the Tweedie Model, by Glenn Meyers, http://casact.org/newsletter/… Beyond…

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Bristish Statisticians and American Gangsters

February 18, 2013
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Bristish Statisticians and American Gangsters

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 famous in Extreme Value Theory for his theorem (the so-called Fisher-Tippett theorem, which gives the…

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Modélisation des coûts individuels en tarification

February 18, 2013
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Modélisation des coûts individuels en tarification

Avant de terminer le cours sur la tarification, on va parler de la modélisation des coûts individuels. On parlera de lois Gamma et de lois lognormales (sur cette dernière, je suggère de relire ce qui avait été dit dans le cours de modèles de régression sur les modèles log-linéaires, rappelé dans un court billet publié à l’automne). On parlera aussi de mélanges de lois, et de lois multinomiales. Les transparents…

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From Simpson’s paradox to pies

February 16, 2013
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From Simpson’s paradox to pies

Today, I wanted to publish a post on economics, and decision theory. And probability too… Those who do follow my blog should know that I am a big fan of Simpson’s paradox. I also love to mention it in my econometric classes. It does raise important questions, that I do relate to multicolinearity, and interepretations of regression models, with multiple (negatively correlated) explanatory variables. This paradox has amazing pedogological virtues. I did mention it several…

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