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Beta distribution: trivial question

  1. Sep 23, 2013 #1
    We all know that it is easy to get the beta mean and variance given the parameters α and β of the distribution (http://en.wikipedia.org/wiki/Beta_distribution).

    Can we do right the opposite? I.e. is there any way to go uniquely from mean and variance to the parameters of the beta?
     
  2. jcsd
  3. Sep 23, 2013 #2

    mathman

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    Based on the formulas in the link, the question can be reduced to solving a cubic equation in α or β as a function of the mean and variance. α and β are linear with respect to each other. Therefore there are at most three possible solutions. Since α and β are both required to be > 0, this could eliminate the extra solutions.
     
  4. Sep 23, 2013 #3
    Yes, there's a unique way. Convert the formula for mean into one for [itex]\frac{\beta}{\alpha}[/itex], then use that formula to simplify the variance formula into something linear in [itex]\alpha[/itex] and [itex]\beta[/itex]. Then you'll have two straight-line relationships (one positively sloped, one negatively sloped) between the two parameters.
     
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