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Topic: Combining Distributions (multiply, dividing etc)
Replies: 1   Last Post: Jun 7, 2009 4:57 PM

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phubaba

Posts: 4
Registered: 2/11/08
Re: Combining Distributions (multiply, dividing etc)
Posted: Jun 7, 2009 4:55 PM
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Okay I figured it out on my own.

For any people reading this. The basic idea is

we have X=Z/W. We can find the distribution of X|W=w for example using the following formula:

Given a function Y=h(X), the distribution of Y is as follows
f_y(y)=f_x(h^-1(y))|dh^-1(x)/d(x)|

so we can use X=h(Z) where h(x)=x/w.

then f_X|W(x|w)=e^(-w*x)*w (from the above formula)

then we can find f_X by integrating out w

f_x=integral(f_X|W(x|w)*f(w)*dw)

in this case f(w) is gamma(alpha,beta) and dw goes from 0 to infinity.

good reference is http://www.ebyte.it/library/docs/math04a/PdfChangeOfCoordinates04.html


Message was edited by: Robert Forler



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