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In his post, one of our colleagues asked if it is possible to find the shape parameters of a $Beta(\alpha,~\beta)$ distribution given knowledge about its $\mu~(mean)$ and $variance$.

However, my question is how in R I can find shape parameters of a $Beta(\alpha,~\beta)$ distribution given only its quantiles (say, lower quantile is "$x = some~known~number$" and upper quantile is "$y = some~known~number$")?

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marked as duplicate by Glen_b distributions Apr 10 '17 at 1:25

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ The indicated duplicate was offered in "Related" before I marked it as a duplicate, which suggests that it would have been one of the posts offered to you as potentially answering your question before you posted. $\endgroup$ – Glen_b Apr 10 '17 at 1:29
  • $\begingroup$ @Glen_b, Sorry are you sure the question you're referring to as being exactly similar to mine is answering my question, because I think that question is a bit different? To be exact that question is talking about a scaled, recentered Beta. My question is about an ordinary Beta. Could you please clarify? $\endgroup$ – rnorouzian Apr 10 '17 at 1:42
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    $\begingroup$ @parvin It solves a problem of which yours is a special case. The very first step of whuber's solution converts it to your standard beta problem. The rest of the answer is the actual solution to your problem. If it completely solves the thing you asked about (it does -- indeed if you put L=0, U=1 you can follow all the steps there) then it's a duplicate. $\endgroup$ – Glen_b Apr 10 '17 at 2:12
  • $\begingroup$ As far as I can see, it's fully answered there. Indeed once it's marked as a duplicate, if I had any answer, I'm supposed to post it in the other thread, not here (indeed I can't post one here at all). My short answer there would consist of "read whuber's excellent answer, which deals with this relatively* complicated problem in detail". *(compared to doing it from moments say)... such an answer would rightly be deleted. If you have a specific question about that post you can post a new question and link to that one, or if you seek a small clarification, you can post a comment and ask. $\endgroup$ – Glen_b Apr 10 '17 at 2:25
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    $\begingroup$ @Glen_b, thank you got you, ok, yes the whole point is that to provide some specified quantiles, and get the required alpha and beta. This is really a need to specify a beta prior. $\endgroup$ – rnorouzian Apr 10 '17 at 4:22