How do I calculate the parameters of the beta distribution from the mean and the variance?

Asked May 12 '20 at 22:59

Active May 13 '20 at 02:40

Viewed 43 times

My mean is 10 and the variance is 4.

There has been confusion around the bounds of $\mu$ and $\sigma_2$ for any given Beta distribution, what I understand is,

$$ \mu = \dfrac{\alpha}{\alpha + \beta} \in (0, 1)$$ $$ \sigma_2 = \dfrac{\alpha \beta}{2 (\alpha + \beta)(\alpha + \beta + 1)} = \dfrac{\mu (1 - \mu)}{\alpha + \beta + 1} < \dfrac{\mu(1 - \mu)}{1}$$

edited May 13 '20 at 02:40

algae

asked May 12 '20 at 22:59

Alence Poudel

This question has already been asked. You can refer to this link [https://stats.stackexchange.com/questions/12232/calculating-the-parameters-of-a-beta-distribution-using-the-mean-and-variance?rq=1] – Sankalp Sharma May 13 '20 at 00:26
@SankalpSharma but I want to know it if the mean is 10 and variance is 4. – Alence Poudel May 13 '20 at 16:26
1

A beta distribution is concentrated on the interval $[0,1]$ so how can its mean be outside that interval? – kjetil b halvorsen May 13 '20 at 18:31

How do I calculate the parameters of the beta distribution from the mean and the variance?

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