How to back-calculate the values of $\alpha$ and $\beta$ of beta function?

Asked Mar 17 '20 at 14:03

Active Mar 17 '20 at 14:43

Viewed 40 times

Modify from this question, if my beta distribution has the following prior:

$$f_{\Theta }(\theta )= a\theta (1-\theta )^2,\textrm{for}\ \theta\in [0,1],$$

and knowing that:

$$\int\limits_0^1\theta^\alpha (1-\theta )^{\beta }\, d\theta =\frac{\alpha !\, \beta !}{(\alpha +\beta +1)!}$$

How do I back-calculate the values of $\alpha$ and $\beta$ ? Thanks.

edited Mar 17 '20 at 14:43

asked Mar 17 '20 at 14:03

muxo

1

$f_{\Theta }(\theta )$ looks rather like a probability distribution depending on parameter $\theta$ and the question could be rather to find $a$. $\alpha$ and $\beta$ are already given. Just look. – trancelocation Mar 17 '20 at 14:12
I was hoping to find $\alpha$ and $\beta$ to calculate $a$. – muxo Mar 17 '20 at 14:13
Look at the exponents and note that $\theta = \theta^1$. Then plug these two exponents into the given formula for the integral. – trancelocation Mar 17 '20 at 14:14
1

So $\alpha = 1$ and $\beta = 2$? – muxo Mar 17 '20 at 14:18
1

You got it! :-) – trancelocation Mar 17 '20 at 14:19
My lord, you saved the day! xD – muxo Mar 17 '20 at 14:20

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