Beta Function used in Beta distribution

[justin001]

Could anyone explain in laymen terms what really the beta function does as said in Beta Function:https://en.wikipedia.org/wiki/Beta_function .I know that gamma function is used to find the factorial of real numbers but when it comes to beta function I can't get what really beta function does.I am reading an article: Empirical Analysis:http://1drv.ms/1GUqmdO:and it explains about Dirichlet distribution:https://en.wikipedia.org/wiki/Dirichlet_distribution

After looking for the prerequisites needed to study Dirichlet distribution as said in Prerequisites for Dirichlet distribution:http://www.metacademy.org/graphs/concepts/dirichlet_distribution#focus=5zwsgm7z&mode=explore I have reached up to Beta distribution:https://en.wikipedia.org/wiki/Beta_distribution in the tree.This is where the beta function comes in beta distribution and that's where I'm stuck.Could anyone help me.

I would like an answer that doesn't uses too much symbols,concepts and jargon terms.I would like a simple explanation for Beta function and how it is used in Beta distribution.

 

[Stephen Tashi]

Since you're reading Bayesian material, try this explanation: http://www.statlect.com/beta_distribution.htm

 

[WWGD]

Maybe this will give you some context:

http://math.stackexchange.com/search?q=Beta+Function

 

[justin001]

Since you're reading Bayesian material, try this explanation: http://www.statlect.com/beta_distribution.htm

I have went through all of these many times before but the concept that get my head stuck is normalization in beta distribution.I would like to know how normalization takes place in beta distribution.Is it(normalization) done by the beta function alone or is there any other factor involved?Also I can't see anything related to Bayesian here.Did you mean to say about conditional probability?

 

[Stephen Tashi]

I can't see anything related to Bayesian here.

The explanation gives an example where the beta distribution is the posterior distribution when a uniform prior on [0,1] is assumed ( a Bayesian approach) and particular data is observed.

 

[justin001]

The explanation gives an example where the beta distribution is the posterior distribution when a uniform prior on [0,1] is assumed ( a Bayesian approach) and particular data is observed.

I think that's too heavy for an novice in Bayesian statistics.Could you show an example by plugging the values α and β that might give an intuition into how beta distribution works.

 

[chiro]

Look up the Beta Integral and by taking out the constant not related to the integral you will see that you get a Beta function back as a result.

Hence the name Beta distribution.