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Re: a question about Hazard Rate - HazardRate.nb (1/1)

• To: mathgroup at smc.vnet.net
• Subject: [mg39990] Re: a question about Hazard Rate - HazardRate.nb (1/1)
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 14 Mar 2003 04:45:17 -0500 (EST)
• Organization: The University of Western Australia
• References: <b4pg49$c0a$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <b4pg49$c0a$1 at smc.vnet.net>,
 "Michael \(Xiaoquan\) Zhang" <zxq at nullvoid.mit.edu> wrote:

> 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.  

After re-scaling one can eliminate beta. The roots of your equation are, 
to a very good approximation, linear in alpha.

See the attached Notebook for more detail.
[Contact Paul directly to get the notebook -moderator]

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
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