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!

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- December 3rd 2008, 05:51 PMplatinumpimp68plus1Deriving expected value and variance of beta distribution
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!

- December 3rd 2008, 06:42 PMmr fantastic
Start by reading this thread: http://www.mathhelpforum.com/math-he...ion-62210.html

- December 4th 2008, 08:30 AMplatinumpimp68plus1
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. :)

- December 6th 2008, 02:11 AMmr fantastic
- November 9th 2009, 01:03 AMziguri
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,

Ziguri

BTW: i already read through all the links you mentioned in this post. - November 9th 2009, 01:45 AMmr fantastic
- March 3rd 2010, 02:45 PMbuster
- March 3rd 2010, 03:04 PMmatheagle
- March 3rd 2010, 11:23 PMbuster
--I don't think that is what I am searching for. Let me try to explain the problem more clearly...

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?

- February 14th 2011, 11:13 AMuniquebatgirl
- February 14th 2011, 08:18 PMmr fantastic
- February 14th 2011, 11:32 PMCaptainBlack