Blog Archives

On Box-Cox transform in regression models

November 13, 2012
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On Box-Cox transform in regression models

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...

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Why pictures are so important when modeling data?

October 31, 2012
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Why pictures are so important when modeling data?

(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 **...

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Fractals and Kronecker product

October 17, 2012
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Fractals and Kronecker product

A few years ago, I went to listen to Roger Nelsen who was giving a talk about copulas with fractal support. Roger is amazing when he gives a talk (I am also a huge fan of his books, and articles), and I really wanted to play with that concept ...

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Compound Poisson and vectorized computations

October 12, 2012
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Compound Poisson and vectorized computations

Yesterday, I was asked how to write a code to generate a compound Poisson variables, i.e. a series of random variables  where  is a counting random variable (here Poisson disributed) and where the 's are i.i.d (and ind...

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Bounding sums of random variables, part 1

September 27, 2012
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Bounding sums of random variables, part 1

For the last course MAT8886 of this (long) winter session, on copulas (and extremes), we will discuss risk aggregation. The course will be mainly on the problem of bounding  the distribution (or some risk measure, say the Value-at-Risk) for two random variables with given marginal distribution. For instance, we have two Gaussian risks. What could be be worst-case scenario...

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Maximum likelihood estimates for multivariate distributions

September 22, 2012
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Maximum likelihood estimates for multivariate distributions

Consider our loss-ALAE dataset, and - as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, > library(evd) > data(lossalae) > Z=lossalae > X=Z;Y=Z ...

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Maximum likelihood estimates for multivariate distributions

September 22, 2012
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Maximum likelihood estimates for multivariate distributions

Consider our loss-ALAE dataset, and – as in Frees & Valdez (1998) - let us fit a parametric model, in order to price a reinsurance treaty. The dataset is the following, > library(evd) > data(lossalae) > Z=lossalae > X=Z;Y=Z The first step can be to estimate marginal distributions, independently. Here, we consider lognormal distributions for both components, > Fempx=function(x) mean(X<=x) >...

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Interactive 3d plot, in R

September 20, 2012
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Interactive 3d plot, in R

Following the course of this afternoon, I will just upload some codes to make interactive 3d plots, in R. > library(rgl) > library(evd); > data(lossalae) > U=rank(lossalae+rnorm(nrow(lossalae), + mean=0,sd=.001))/(nrow(lossalae)+1) ...

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(nonparametric) Copula density estimation

September 20, 2012
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(nonparametric) Copula density estimation

Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related things).  Consider (as before) the loss-ALAE data...

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(nonparametric) copula density estimation

September 19, 2012
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(nonparametric) copula density estimation

Today, we will go further on the inference of copula functions. Some codes (and references) can be found on a previous post, on nonparametric estimators of copula densities (among other related things).  Consider (as before) the loss-ALAE dataset (since we’ve been working a lot on that dataset) > library(MASS) > library(evd) > X=lossalae > U=cbind(rank(X)/(nrow(X)+1),rank(X)/(nrow(X)+1)) The standard tool to plot...

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