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...
Blog Archives
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...
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 ...
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) >...
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) ...
(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...
(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...
Copulas and tail dependence, part 3
We have seen extreme value copulas in the section where we did consider general families of copulas. In the bivariate case, an extreme value can be writtenwhere is Pickands dependence function, which is a convex function satisfyingObserve that in ...
Copulas and tail dependence, part 2
An alternative to describe tail dependence can be found in the Ledford & Tawn (1996) for instance. The intuition behind can be found in Fischer & Klein (2007)). Assume that and have the same distribution. Now, if we assume that those vari...
Copulas and tail dependence, part 1
As mentioned in the course last week Venter (2003) suggested nice functions to illustrate tail dependence (see also some slides used in Berlin a few years ago). Joe (1990)'s lambda Joe (1990) suggested a (strong) tail dependence index. For lower t...
Zero Inflated Models and Generalized Linear Mixed Models with R.
Zuur, Saveliev, Ieno (2012).
