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phubaba
Posts:
4
Registered:
2/11/08


Re: Combining Distributions (multiply, dividing etc)
Posted:
Jun 7, 2009 4:55 PM


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 XW=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_XW(xw)=e^(w*x)*w (from the above formula)
then we can find f_X by integrating out w
f_x=integral(f_XW(xw)*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



