How to write a non-standard (four parameter) beta pdf as a symbolic expression?

Hi there, new to matlab, would appreciate any help!

I want to write an expression for a 4 parameter beta probability density function in matlab.

Here's what I wrote:

syms x a b q r assume(q>0 & r>0 & a<=u<=b) pd = (((x-a)^(q-1))*((b-x)^(r-1)))/(beta(q,r))*((b-a)^(q+r-1))

I thought I'd check to see if this made sense, by integrating the expression over a support and checking to see it returned 1. I took the following values: a=0.3 (lower bound) b= 1 (upper bound) q=r=2 (shape parameters)

int(pd,x,0.3,1)

unfortunately, I don't get 1 as an answer!

Answer 1

[Torsten]

pd = (x-a)^(q-1)*(b-x)^(r-1)/(beta(q,r)*(b-a)^(q+r-1))

Best wishes

Torsten.