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 ... [Read more...]

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 ... [Read more...]

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~... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

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 ... [Read more...]

Let us continue our discussion on smoothing techniques in regression. Assume that . where is some unkown function, but assumed to be sufficently smooth. For instance, assume that  is continuous, that exists, and is continuous, that  exists and is also continuous, etc. If  is smooth enough, Taylor’s expansion can be ... [Read more...]

In a standard linear model, we assume that . Alternatives can be considered, when the linear assumption is too strong. Polynomial regression A natural extension might be to assume some polynomial function, Again, in the standard linear model approach (with a conditional normal distribution using the GLM terminology), parameters can be ... [Read more...]

I admit it, the title sounds weird. The problem I want to address this evening is related to the use of the stepwise procedure on a regression model, and to discuss the use of categorical variables (and possible misinterpreations). Consider the following dataset __ db = read.table("http://freakonometrics.free.fr/... [Read more...]

To get back to a question asked after the last course (still on non-life insurance), I will spend some time to discuss ROC curve construction, and interpretation. Consider the dataset we’ve been using last week, __ db = read.table("http://freakonometrics.free.fr/db.txt",header=TRUE,sep=";") __ attach(db) ... [Read more...]

A series of tutorials, in R, by Anthony Damico. As claimed on http://twotorials.com/, “how to do stuff in r. two minutes or less, for those of us who prefer to learn by watching and listening“. So far, 000 what is r? the lingua statistica, s’il vous plaît 001 ... [Read more...]

A short post to get back – for my nonlife insurance course – on the interpretation of the output of a regression when there is a categorical covariate. Consider the following dataset __ db = read.table("http://freakonometrics.free.fr/db.txt",header=TRUE,sep=";") __ tail(db) Y X1 X2 X3 995 1 4.801836 20.82947 A 996 1 9.867854 24.39920 C 997 1 5.390730 21.25119 ... [Read more...]

Quite frequently, someone on the internet discovers the Monty Hall paradox, and become so enthusiastic that it becomes urgent to publish an article – or a post – about it. The latest example can be http://www.bbc.co.uk/news/magazine-24045598. I won’t blame them, I did the same a ... [Read more...]

This morning, in the ACT2040 class (on non-life insurance), we’ve discussed the difference between observable and non-observable heterogeneity in ratemaking (from an economic perspective). To illustrate that point (we will spend more time, later on, discussing observable and non-observable risk factors), we looked at the following simple example. Let  ... [Read more...]

This morning, Benoit sent me an email, about an exercise he found in an econometric textbook, about linear regression. Consider the following dataset, Here, variable X denotes the income, and Y the expenses. The goal was to fit a linear regression (actually, in the email, it was mentioned that we ... [Read more...]

Yesterday evening, I wanted to play with Twitter, and see which websites I was using as references in my tweets, to get a Top 4 list. The first problem I got was because installing twitteR on Ubuntu is not that simple ! You have to install properly RCurl… But you before install ... [Read more...]

I always claim that graphs are important in econometrics and statistics ! Of course, it is usually not that simple. Let me come back to a recent experience. A got an email from Sami yesterday, sending me a graph of residuals, and asking me what could be done with a graph ... [Read more...]

Iin insurance pricing, the exposure is usually used as an offset variable to model claims frequency. As explained many times on this blog (e.g. here), and in my notes, if we have to identical drivers, but one with an exposure of 6 months, and the other one of one year, ... [Read more...]

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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 ... [Read more...]