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

[Sahasrabuddhe, Rajesh]

Ralph - So I think what you need to fit is a mixture of Pareto distributions (assuming the numbers of components is both finite and relatively small.) The Poisson will be relatively straightforward.
There is an R package to fit mixtures (I think it's mixtools) but I don’t believe that it supports Pareto mixtures.

I have become a big fan of fitting using Bayesian techniques via JAGS - but that is a decision that you will need to make.

Thanks - Raj





Rajesh Sahasrabuddhe
Oliver Wyman
Three Logan Square
1717 Arch Street, Suite 1100
Philadelphia, PA 19103
Phone:  +1 215 246 1028
Cell:  +1 610 209 0143
Fax:  +1 215 246 1399
rajesh.sahasrabuddhe at oliverwyman.com
www.oliverwyman.com


Please consider the environment before printing.


-----Original Message-----
From: R-SIG-insurance [mailto:r-sig-insurance-bounces at r-project.org] On Behalf Of Ralph Scherer
Sent: Thursday, August 13, 2015 7:39 AM
To: Christophe Dutang
Cc: r-sig-insurance at r-project.org
Subject: Re: [R-sig-ins] Estimate Pareto parameter from compound distribution

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/Charpe
> ntier/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
>>
>> _______________________________________________
>> R-SIG-insurance mailing list
>> R-SIG-insurance at r-project.org
>> https://stat.ethz.ch/mailman/listinfo/r-sig-insurance
>
>

_______________________________________________
R-SIG-insurance mailing list
R-SIG-insurance at r-project.org
https://stat.ethz.ch/mailman/listinfo/r-sig-insurance

This email and any attachments may be confidential or proprietary. Any review, use, disclosure, distribution or copying of this email is prohibited except by or on behalf of the intended recipient. If you received this message in error or are not the intended recipient, please delete or destroy the email message and any attachments or copies and notify the sender of the erroneous delivery by return email. To the extent that this message or its attachments were sent without encryption, we cannot guarantee that the contents have not been changed or tampered with. Any advice expressed in this message is being delivered to you solely for your use in connection with the matters addressed herein and may not be used for any other purpose without our prior written consent.