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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.