This morning, Mathieu had a nice experience in his course on computational method in actuarial science. But let us start with some mathematical formal definitions. First, recall that is – somehow – a standard expression. No one should be surprised to see such an expression. Generally (as explained in http://en.wikipedia.... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

This morning, I was working on some paper on inequality measures, and for computational reasons, I had to sort elements in a matrix. To make it simple, I had a rectangular matrix, like the one below, __ set.seed(1) __ u=sample(1:(nc*nl)) __ (M1=matrix(u,nl,nc)) [,1] [,2] [,3] [,4] [,5] [,6] [1,] 7 5 11 23 6 17 [2,] 9 18 1 21 24 15 [3,] 13 19 3 8 22 2 [4,] 20 12 14 16 4 10 I had to ... [Read more...]

During the course, we have seen that it is natural to assume that not only the individual claims frequency can be explained by some covariates, but individual costs too. Of course, appropriate families should be considered to model the distribution of the cost , given some covariates .Here is the dataset ... [Read more...]

Last week, we’ve seen how to take into account the exposure to compute nonparametric estimators of several quantities (empirical means, and empirical variances) incorporating exposure. Let us see what can be done if we want to model a binomial response. The model here is the following: , the number of ... [Read more...]

Yesterday, I was uploading some old posts to complete the migration (I get back to my old posts, one by one, to check links of pictures, reformating R codes, etc). And I re-discovered a post published amost 2 years ago, on nuns and Hell’s Angels in an airplaine. It reminded ... [Read more...]

Next Friday, I will give in Montréal a crash course entitled Econometric Modeling in Finance and Insurance with the R Language. Since IFM2 wanted this course to be an opportunity to discover R, the first part o fthe course will be on the R language. Slides can be downloaded ... [Read more...]

(see John Wilkins’ article on the – interesting – history of that phrase http://scienceblogs.com/evolvingthoughts/…). We will see, this week in class, several smoothing techniques, for insurance ratemaking. As a starting point, assume that we do not want to use segmentation techniques: everyone will pay exactly the same price. no ... [Read more...]

Consider the following time series, What does it look like ? I know, this is a stupid game, but I keep using it in my time series courses. It does look like a random walk, doesn’t it ? If we use Philipps-Perron test, yes, it does, __ PP.test(x) Phillips-Perron Unit ... [Read more...]

In actuarial science, and insurance ratemaking, taking into account the exposure can be a nightmare (in datasets, some clients have been here for a few years – we call that exposure – while others have been here for a few months, or weeks). Somehow, simple results because more complicated to compute just ... [Read more...]

This morning, Stéphane asked me tricky question about extracting coefficients from a regression with categorical explanatory variates. More precisely, he asked me if it was possible to store the coefficients in a nice table, with information on the variable and the modality (those two information being in two different ... [Read more...]

In insurance, the law of large numbers (named loi des grands nombres initially by Siméon Poisson, see e.g. http://en.wikipedia.org/…) is usually mentioned to legitimate large portfolios, because of pooling and diversification: the larger the pool, the more ‘predictable’ the losses will be (in a given ... [Read more...]

In order to illustrate the construction of regression tree (using the CART methodology), consider the following simulated dataset, __ set.seed(1) __ n=200 __ X1=runif(n) __ X2=runif(n) __ P=.8*(X1.7) __ Y=rbinom(n,size=1,P) __ B=data.frame(Y,X1,X2) with one dichotomos varible (the variable of interest, ), and two ... [Read more...]

As mentioned in the Appendix of Modern Actuarial Risk Theory, “R (and S) is the ‘lingua franca’ of data analysis and statistical computing, used in academia, climate research, computer science, bioinformatics, pharmaceutical industry, customer analytics, data mining, finance and by some insurers. Apart from being stable, fast, always up-to-date and ... [Read more...]

Following my previous post, a few more things. As mentioned by Frédéric, it is – indeed – possible to compute the probability of all pairs. More precisely, all pairs are not as likely to occur: some teams can play against (almost) eveyone, while others cannot. From the previous table, it ... [Read more...]

Ok, I was supposed to take a break, but Frédéric, professor in Tours, came back to me this morning with a tickling question. He asked me what were the odds that the Champions League draw produces exactly the same pairings from the practice draw, and the official one (... [Read more...]

A few days ago, a former student of mine, David, contacted me about Box-Cox tests in linear models. It made me look more carefully at the test, and I do not understand what is computed, to be honest. Let us start with something simple, like a linea... [Read more...]

(bis repetita) Consider the following regression summary,Call: lm(formula = y1 ~ x1)   Coefficients: Estimate Std. Error t value Pr(__|t|) (Intercept) 3.0001 1.1247 2.667 0.02573 * x1 0.5001 0.1179 4.241 0.00217 **... [Read more...]