a question about Hazard Rate

*To*: mathgroup at smc.vnet.net*Subject*: [mg39986] a question about Hazard Rate*From*: "Michael \(Xiaoquan\) Zhang" <zxq at nullvoid.mit.edu>*Date*: Thu, 13 Mar 2003 03:06:17 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi all, I was working on a theoretical model about valuation distribution. Assuming a Gamma distribution (or any other right skewed pdf). I finally got a equation to solve for p: 1=p*f(p)/[1-F(p)] where f(.|alpha, beta) is the pdf of the Gamma distribution, and F(.) is the CDF. alpha and beta are shape and scale parameters for Gamma. I don't have to derive a closed form for p, but I need some properties of p satisfying the equation. Especially, I need the connection between this p and the solution, q, of another equation with g and G substituting f and F. (if this is hard to get in general, how about g(.|a,b)=f(.|n*alpha,beta). (meaning g is only different from f by a parameter alpha, and g's alpha is n times of f's. Thanks in advance.