Posts Tagged ‘ copulas ’

Fractals and Kronecker product

October 17, 2012
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$T=\frac{1}{8}\left(\begin{matrix}1& 0 & 1 \\ 0 & 4 & 0 \\ 1 & 0&1\end{matrix}\right)$

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 ...

(nonparametric) Copula density estimation

September 20, 2012
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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...

Copulas and tail dependence, part 3

September 18, 2012
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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 1

September 17, 2012
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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...

Kendall’s function for copulas

September 12, 2012
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As mentioned in the course on copulas, a nice tool to describe dependence it Kendall's cumulative function. Given a random pair with distribution  , define random variable . Then Kendall's cumulative function is Genest and Rivest (1993) intr...