Product of two Beta distributed random variables

Question

I have two Beta distributed random variables :

$X_1=B(\alpha_1, \beta_1)$

$X_2=B(\alpha_2, \beta_2)$

What can we say about $Y=X_1.X_2$? Is this also a Beta distributed random variable?

Answer 1

You can have a look at the following paper http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2012/7_12.pdf which tackles your problem

Answer 2

There are several paper for this problem. See for example:

• On the Distribution of the Product of Independent Beta Random Variables – Applications
• Products of Beta distributed random variables
• BETA PRODUCTS WITH COMPLEX PARAMETERS