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Math Help - Rearrange terms in two equations: Beta distribution mean/var

  1. #1
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    Rearrange terms in two equations: Beta distribution mean/var

    Hello,

    The beta distribution has
    mean = a/(a+b)
    variance = ab/((a+b)^2 * (a+b+1))
    where a and b are shape parameters
    I want to solve for a and b in terms of the mean and variance.

    For example, I want an answer that looks like this
    a = var*mean^2
    b = mean*var
    except I made up these expressions and I want the real ones.

    Thanks a lot for any help.
    J
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  2. #2
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    Quote Originally Posted by FishSqueezer View Post
    Hello,

    The beta distribution has
    mean = a/(a+b)
    variance = ab/((a+b)^2 * (a+b+1))
    where a and b are shape parameters
    I want to solve for a and b in terms of the mean and variance.

    For example, I want an answer that looks like this
    a = var*mean^2
    b = mean*var
    except I made up these expressions and I want the real ones.

    Thanks a lot for any help.
    J
    You have:

    \displaystyle \mu = \frac{a}{a + b} .... (1)


    \displaystyle \sigma^2 = \frac{ab}{(a + b)^2(a + b + 1)} .... (2)


    and you want to solve a and b in terms of \mu and \sigma^2.

    Is that so?
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  3. #3
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    Yeah, that's what I was hoping to do. This would allow me to calculate the parameters needed to produce a desired mean and variance in the distribution. I'm just hung up on the Algebra.

    Thanks
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  4. #4
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    WolframAlpha was able to solve this system of equations.
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  5. #5
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    Thanks

    Thanks a lot for the help!
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