Is this theoretical or do you have data?
Hello, I having doubts on this issue
1) If X~Gamma(a,B) and Y~Beta(γ,B-γ), respectively with B>= 0 and γ>= 0, such that
γ <= B. Which distribution Z= XY?
I tried Jacobian, convolution integral, but I can not get anything
Is this theoretical or do you have data?
Stop cowardice, ban guns!
This is theoretical, I need to find the distribution of Z=XY.
I did this BGM, but I can not get somewhere.
Did Z= XY and W = Y, calculated the Jacobian and find the fZ, W (z, w) (joint distribution),
but when I make a marginal, fz (z) distribution get caught.
Last edited by askazy; 11-21-2014 at 01:57 PM.
Ok just search the question a little bit and this is a well-known result. The problem is that there is a typo in the question:
Let and they are independent. Then
The key fact here is that the sum of the two Beta's parameters need to equal to the shape parameter of the Gamma distribution. Otherwise there will be no nice result.
Continue your integration with some careful simplifications and a change of variable, then it will be done. I have just verified it once.
Yes as I said I have did it on rough paper completely (and already thrown away). Anyway you are in the correct direction for the convolution step and the remaining task is just a simple integrating process. It is not hard. It will be better to show which part you stuck at.
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