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]