Re: [R] Solving Systems of Non-linear equations

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Thu 01 Dec 2005 - 03:05:14 EST

On 11/30/2005 10:14 AM, Scott Story wrote:
> I am trying to write a function that will solve a simple system of
> nonlinear equations for the parameters that describe the beta
> distribution (a,b) given the mean and variance.
>
>
> mean = a/(a+b)
> variance = (a*b)/(((a+b)^2) * (a+b+1))
>
> Any help as to where to start would be welcome.

You should use a package like Maple or Mathematica (or just some pencil and paper work) to determine the solution. Then the function is really easy to write.

Maple gives

 > solve({mean = a/(a+b),variance = (a*b)/(((a+b)^2) * (a+b+1))},{a,b});

{a = -mean*(variance+mean^2-mean)/variance,   b = (variance+mean^2-mean)*(mean-1)/variance}

from which you can write your own function pretty easily.

Duncan Murdoch



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