Talk:Panjer recursion

Merger proposal

Copied from Wikipedia talk:WikiProject Statistics#Another article to consider:

I have come across the article (a,b,0) class of distributions which is untouched for some time and has essentailly no articles linking to it. Questions are: Is there a better name for this? Is it just a special case of something else? Melcombe (talk) 09:04, 16 June 2009 (UTC)[reply]

Never heard of it before, but it appears to be the same thing as Panjer recursion#Claim number distribution. Merge? Note that Panjer class already redirects to this section. Google reveals that Panjer defined an (a,b,1) class too, but Wikipedia appears to have nothing on that at present. Qwfp (talk) 10:28, 16 June 2009 (UTC)[reply]

Please continue discussion below. Qwfp (talk) 11:02, 16 June 2009 (UTC)[reply]

This has prompted me to look in Johnson,Kotz & Kemp's book on Univariate Discrete distributions ... the "(a,b,0) class of distributions" seems to be identical to what they call the "Katz family" due to Katz's work over 1945-65, and which is a special case of a family worked on by Carver 1919-25. Ord's book "Families of Frequency Distributions" covers the general case of Carver and I think identifies the "(a,b,0) class of distributions" as a special case which he calls type III without associating anyone's name with it. It seems there may be enough known about these distributions to have results for moments and estimation in an article on the distribution. What is not clear at prresent is whether the more general form of "Panjer recursion" is different from Carver's family of distributions, which is also given in recursive form, but it seems it must be. Melcombe (talk) 12:39, 16 June 2009 (UTC)[reply]

Here are my thoughts. Exam C of preliminary exams of the Society of Actuaries has questions about the (a,b,0) (and by extension (a,b,m) distributions). The SOA uses Loss Models as the main (and almost only) required material for studying Exam C (along with Derivatives Markets which accounts for the financial and simulation questions of the exam). Loss Models is co-authored by Panjer. On the other hand, I'll note that nowhere does (or did) the SOA use any other way of calling it than (a,b,0) (or (a,b,1)...) class of distributions.

I should also note that for quite some time now I've been thinking about adding a section to the article which would be called something like (a,b,m) distributions, which would address the remarks made about (a,b,1) distributions. Basically, an (a,b,1) distribution is simply a distribution of the (a,b,0) family that has its $p_0$ weight fixed, and the other weights being proportionally adjusted. You might also want to fix $p_1$, $p_2$, etc. In those cases, the recursive relationship only starts after the last fixed weight.

The only reason why I have no clear or final opinion on the issue is basically because I've never heard of "Panjer's" thingy or the "Katz family" and other stuff like that, so I can't determine whether having a separate article makes sense or not. However, because the SOA is the governing body for actuarial in the United States, as well as a big part of it in Canada and Mexico, I'd suggest trying to keep in line with what they use, unless other actuarial societies (in the UK or in Australia, for instance) use something else.

Well, those were my two cents. :) Seigneur101 (talk) 13:36, 16 June 2009 (UTC)[reply]