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

[Ralph Scherer]

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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>
>