[R-sig-ins] Estimate Pareto parameter from compound distribution

[Christophe Dutang]

Dear all,

If you know the targeted distribution (empirical?), you can still simulate 1e6 random variates and fit a compound Poisson-Pareto (via pkg Compounding) with fitdistrplus.

Regards, Christophe
---------------------------------------
Christophe Dutang
LMM, UdM, Le Mans, France
web: http://dutangc.free.fr

Le 13 août 2015 à 13:39, Ralph Scherer <shearer.ra76 at gmail.com> a écrit :

> Dear Rajesh, dear Christophe,
> 
> thank you both for the fast replies.
> Quantile matching sounds good for the problem, when there is only one
> distribution in the background.
> The problem is that the quantile comes from a distribution which has
> the additional information about the frequency.
> For example the claim from the 0.005 quantile has in addition the
> information about the frequency in form of the lambda parameter of the
> Poisson distribution.
> 
> To my understanding there is then a compound Poisson/Pareto
> distribution in the background and I am interested in estimating the
> Pareto parameters of this distribution.
> 
> The idea of using Bayes statistics sounds interesting for more complex
> distributions, but I hoped that for the Pareto/Poisson distribution an
> easier analytical solution would be possible.
> 
> The idea behind this question is that in some cases we have no
> information about the losses and we make assumptions about the
> quantile and the frequency. Then we are interested in the parameter of
> the underlying distribution.
> 
> Best Wishes
> Ralph
> 
> 
> 
> 2015-08-13 8:40 GMT+02:00, Christophe Dutang <dutangc at gmail.com>:
>> Dear Ralph,
>> 
>> I think you are looking for quantile matching estimation, which is providing
>> in the fitdistrplus package.
>> 
>> Here is an example
>> 
>> library(actuar)
>> library(fitdistrplus)
>> 
>> data(danishuni)
>> x <- danishuni$Loss
>> 
>> args(dpareto)
>> summary(x)
>> 
>> f1 <- fitdist(x, "pareto", method="qme", probs=c(5/1000, 1/10), start =
>> list(shape=10, scale=10))
>> 
>> cdfcomp(f1, do.points=FALSE, xlogscale=TRUE)
>> 
>> 
>> On the danish example, one should use a 3-parameter distribution such as
>> Burr.
>> 
>> See also the book of Arthur Charpentier :
>> https://www.crcpress.com/Computational-Actuarial-Science-with-R/Charpentier/9781466592599
>> 
>> Regards, Christophe
>> ---------------------------------------
>> Christophe Dutang
>> LMM, UdM, Le Mans, France
>> web: http://dutangc.free.fr
>> 
>> Le 12 août 2015 à 20:38, Ralph Scherer <shearer.ra76 at gmail.com> a écrit :
>> 
>>> Dear list members,
>>> 
>>> I know the value of the 0.005 percentile of a compound claim distribution
>>> (Pareto/ Poisson).
>>> Further I know the frequency of the percentile value which is for example
>>> 1/10.
>>> 
>>> I am searching a formula and/or R code to calculate the parameter of the
>>> underlying Pareto distribution..
>>> Does anybody know a solution for the problem?
>>> 
>>> Best Wishes
>>> Ralph
>>> 
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>>> R-SIG-insurance mailing list
>>> R-SIG-insurance at r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-insurance
>> 
>>