1
$\begingroup$

Consider the regularized incomplete beta function $I_x(a, b)$ with $x \in [0,1]$ and $a, b > 0$. I am hypothesizing that the function is monotone decreasing with respect to $a$ and monotone increasing with respect to $b$, but I have had a hard time proving or disproving it. I believe this to be true because of the behavior of the beta distribution, and I haven't found any counterexamples from computation.

I noticed that this post addresses a similar problem, but I don't see how the method can be adapt to my problem directly, since the core construction is to find a change of variable so that the top and bottom integral are on the same interval.

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

By looking through google results once more, I found the desired result in theorem 1 of this paper.

Improve this answer
$\endgroup$

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.