I know what they are, but I don't understand how to derive them from the probability mass function. Any help/hints would be much appreciated!
All right thanks, I read through that and it shed some light. At least now I understand where the normalizing constant comes from! But I tried solving again using similar methods and I'm still stuck. The problem for me is that the solution in that thread is working from the gamma->beta direction but I have to solve (or at least I think?) from the opposite direction and I can't seem to wrap my head around it. I'm in the mind frame of E[X] = integral xf(x) and I don't know where I'm supposed to put the x or really how to proceed from there. If you could give me a push in the right direction (ie. where do I start?) I'd be very thankful.
Dear Mr Fantastic.
Would you please be so kind and give me a hint how you solved your last step in the proof.
The one with the comment: "using the well known property of the Gamma function"
Thanks a lot,
BTW: i already read through all the links you mentioned in this post.
standard beta distribution is defined from 0 to 1 and has the pdf_1 =
f(x;a,b) = [1 / B(a,b)] * x^(a - 1) * (1 - x)^(b - 1)
-where 'a' and 'b' are the alpha and beta parameters respectively
but the generalized beta function has the pdf_2=
f(x;a,b,c,d) = [1 / B(a,b)] * [1 / (d - c)^(a + b - 1)] * (x - c)^(a - 1) * (d - x)^(b - 1)
-where 'c' and 'd' are the min and max scale parameters respectively. I believe they are supposed to scale the original distribution (having 0 to 1 range) to the specified c to d range distribution.
The question I have is in two parts...
1) How is the pdf_2 derived?
2) How to derive the expected value using pdf_2?