Page 64 of Hogg/Klugman has the histogram p.d.f. formula;
h(x) = (n(i)/n)*(1/(c(i) - c(i-1)); for x in the interval c(i-1) < x <=
c(i)
The second moment on the interval is the expected value of x^2 over the
interval, so all you have to do is integrate x^2*h(x) from c(i-1) to c(i).
You will need to use the difference of cubes factorization to simplify the
result to the form in Klugmans review note.
Dave Kennerud
kennerud@concentric.net
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> From: Annette Thomas <annette.thomas@infinity-insurance.com>
> To: studygroup4b@lists.casact.org
> Subject: Klugman Loss Distribution review
> Date: Thursday, August 20, 1998 8:56 AM
>
> The following formula is my attempt to reproduce that presented in
> Klugman's Loss Distribution review (page 24, ans. #3). I need more
> direction on this. Where is it located in the syllabus readings?
>
> n(i)[(c(i))^2+c(i)*c(i-1)+(c(i-1))^2]/3n
>