Blog Archives

Reserving with negative increments in triangles

April 11, 2013
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Reserving with negative increments in triangles

A few months ago, I did published a post on negative values in triangles, and how to deal with them, when using a Poisson regression (the post was published in French). The idea was to use a translation technique: Fit a model not on ‘s but on , for some , Use that model to make predictions, and then...

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Easter

March 31, 2013
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Easter

This morning, there was an interesting post entitled “why does Easter move around so much?” online on http://economist.com/blogs/economist-explains/… In my time series classes, I keep saying that sometimes, series can exhibit seasonlity, but the seasonal effect can be quite irregular. It is the cas for river levels, where snowmelt can have a huge impact, and it is irregular. Similarly, chocolate sales...

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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...

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Rationality, and MS Excel (and other calculators)

March 27, 2013
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Rationality, and MS Excel (and other calculators)

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.org/… ), this function is defined only when . The...

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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...

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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,...

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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...

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Sorting rows and colums in a matrix (with some music, and some magic)

February 14, 2013
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Sorting rows and colums in a matrix (with some music, and some magic)

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)) 7 5 11 23 6 17 9 18 1 21...

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Large claims, and ratemaking

February 13, 2013
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Large claims, and ratemaking

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 we’ll use, > sinistre=read.table("http://freakonometrics.free.fr/sinistreACT2040.txt", + header=TRUE,sep=";") > sinistres=sinistre...

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Exposure with binomial responses

February 9, 2013
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Exposure with binomial responses

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 claims  on the period  is unobserved the number of...

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