Posts Tagged ‘ MAT8886 ’

(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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Kendall’s function for copulas

September 12, 2012
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Kendall’s function for copulas

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...

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MAT8886 the Dirichlet distribution

February 15, 2012
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MAT8886 the Dirichlet distribution

In the course, still introducing some concept of dependent distributions, we will talk about the Dirichlet distribution (which is a distribution over the simplex of ). Let denote the Gamma distribution with density (on ) Let denote independent...

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MAT8886 elliptically contoured distributions

February 15, 2012
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MAT8886 elliptically contoured distributions

(This article was first published on Freakonometrics - Tag - R-english, and kindly contributed to R-bloggers) Last week, we've introduced the concept of exchangeable variables, i.e. satisfying for any matrix  , i.e. is a permutation matrix: belongs to the orthogonal group, , and with elements in . It is possible to extend that family, considering all matrices in the...

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MAT8886 exchangeability, credit risk and risk measures

February 10, 2012
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MAT8886 exchangeability, credit risk and risk measures

Exchangeability is an extremely concept, since (most of the time) analytical expressions can be derived. But it can also be used to observe some unexpected behaviors, that we will discuss later on with a more general setting. For instance, in a old...

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MAT8886 a short word on profile likelihood

February 7, 2012
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MAT8886 a short word on profile likelihood

Profile likelihood is an interesting theory to visualize and compute confidence interval for estimators (see e.g. Venzon & Moolgavkar (1988)). As we will use is, we will plot But more generally, it is possible to consider where . Then (...

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MAT886 mean excess function (and reinsurance)

February 1, 2012
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MAT886 mean excess function (and reinsurance)

Tomorrow, in the course on extreme value, we will focus on applications. We will discuss reinsurance pricing. Consider a random variable , a threshold and define the mean excess function. This function is known in life insurance as the average ...

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MAT8886 Extremes and sums (of i.i.d. random variables)

January 20, 2012
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MAT8886 Extremes and sums (of i.i.d. random variables)

Yesterday, we have discussed briefly sums and maximas of i.i.d. random variables using the concept of subexponential distributions. Today, we will introduce the concept of regular variation: a positive function is said to be regularly varying (at i...

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