# Blog Archives

## Maximum Likelihood versus Goodness of Fit

November 8, 2013
By
$\{X_1,\cdots,X_n\}$

Thursday, I got an interesting question from a colleague of mine (JP). I mean, the way I understood the question turned out to be a nice puzzle (but I have to confess I might have misunderstood). The question is the following : consider a i.i.d. sample of continuous variables. We would like to choose between two (parametric) families for...

## Generating functions

November 8, 2013
By
$F(x)=1-e^{-x}/3$

Today, I wanted to publish a post on generating functions, based on discussions I had with Jean-Francois while having our coffee after lunch a couple of times already. The other reason is that I publish my post while my student just finished their Probability exam (and there were a few questions on generating functions). A short introduction (back on...

## Smoothing mortality rates

November 4, 2013
By

This morning, I was working with Julie, a student of mine, coming from Rennes, on mortality tables. Actually, we work on genealogical datasets from a small region in Québec, and we can observe a lot of volatiliy. If I borrow one of her graph, we get something like Since we have some missing data, we wanted to use some...

## Halloween and candies (a ballot problem)

October 30, 2013
By

This year, for Halloween, a post on candies (I promise, next year I will write another post on zombies). But I don’t want to focus on the kids problems (last year, we tried to minimize their walking distance to collect as much candies as possible, with part 1 and part 2), I want to discuss my own problems. Because usually, the kids wear...

## More significant? so what…

October 30, 2013
By

Following my non-life insurance class, this morning, I had an interesting question from a student, that I will try to illustrate, and reformulate as accurately as possible. Consider a simple regression model, with one variable of interest, and one possible explanatory variable. Assume that we have two possible models, with the following output (yes, I do hide interesting parts...

## Pricing Reinsurance Contracts

October 24, 2013
By

In order to illustrate the next section of the non-life insurance course, consider the following example1, inspired from http://sciencepolicy.colorado.edu/…. This is the so-called “Normalized Hurricane Damages in the United States” dataset, for the period 1900-2005, from Pielke et al. (2008). The dataset is available in xls format, so we have to spend some time to import it, > library(gdata) >...

## GLM, non-linearity and heteroscedasticity

October 22, 2013
By
$Y_i=\beta_0+\beta_1 X_i +\varepsilon_i$

Last week in non-life insurance course, we’ve seen the theory of the Generalized Linear Models, emphasizing the two important components the link function (which is actually the key component in predictive modeling) the distribution, or the variance function Just to illustrate, consider my favorite dataset ­lin.mod = lm(dist~speed,data=cars) A linear model means here where the residuals are assumed to be...

## Equidistant points on a map

October 17, 2013
By

This morning, I had a comment on a recent post, regarding a graph I did upload on the blog, which was extracted from a paper now online (see http://hal.archives-ouvertes.fr/hal-00871883). Jo (from KUL, I guess I can share that piece of information) asked me I was wondering whether you would want to share the R code for plotting figures 1...

## Generating your own normal distribution table

October 15, 2013
By

It might sounds incredibly old fashion, but for my the exam for the ACT2121 probability course (to prepare for the exam P of the Society of Actuaries), I will provide a standard normal distribution table. The problem is that it is never the one we’re looking for (sometimes it is the survival function, sometimes it is the cumulative distribution function,...

## Please, never use my codes without checking twice (at least)!

October 9, 2013
By

I wanted to get back on some interesting experience, following a discussion I had with Carlos after my class, this morning. Let me simplify the problem, and change also the dataset. Consider the following dataset > db = read.table("http://freakonometrics.free.fr/db2.txt",header=TRUE,sep=";") Let me change also one little thing (in the course, we use the age of people as explanatory variables, so...