[R] Solving Systems of Non-linear equations

Martin Maechler maechler at stat.math.ethz.ch
Thu Dec 1 14:55:45 CET 2005

>>>>> "YNoel" == NOEL Yvonnick <yvonnick.noel at uhb.fr>
>>>>>     on Thu, 01 Dec 2005 14:42:44 +0100 writes:

    YNoel> On 11/30/05, Scott Story <sstory at montana.edu> 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.
    YNoel> The simplest way to go is probably to use the fitdistr function in MASS 
    YNoel> package.

yes, definitely for estimating the beta parameters - namely do
something smarter than the above moment estimates.

However, I (and probably most respondents to this thread)
believe that the question was more general (as the subject
indicates) about solving non-lin eq systems, rather than about
estimating the beta parameters (by a sub-optimal method).

Martin Maechler, ETH Zurich

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