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Re: FindDistributionParameters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126782] Re: FindDistributionParameters
  • From: Darren Glosemeyer <darreng at wolfram.com>
  • Date: Thu, 7 Jun 2012 05:19:20 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201205290947.FAA06712@smc.vnet.net> <4FC4DF58.8050808@wolfram.com> <CAKYgLuteC+bm1nGvXRb0GuKcWEkTcySwDuBUJv7HDwz9wPY=xQ@mail.gmail.com>

The initialization is what NMaximize uses by default, so there are no 
starting estimates explicitly given by the distribution parameter 
estimation code. Options can be passed to NMaximize by setting the 
ParameterEstimator option to FindDistributionParameters, e.g. 
ParameterEstimator->{"MaximumLikelihood", Method->{"NMaximize", 
optionsYouWantToPassToNMaximize}.

Darren Glosemeyer
WolframResearch

On 6/6/2012 3:09 PM, Julian Haw wrote:
> Thanks for the response.  How would NMaximize be initialized then?  I 
> know it probably varies by the function, but could you give a typical 
> example of an initialization for a numerical search for an MLE type 
> function?
>
> On Tue, May 29, 2012 at 10:38 AM, Darren Glosemeyer 
> <darreng at wolfram.com <mailto:darreng at wolfram.com>> wrote:
>
>     On 5/29/2012 4:47 AM, Julian wrote:
>
>         I was wondering how FindDistributionParameters chooses an initial
>         point in the MLE search procedure when none is specified.
>          That is,
>         the function numerically fits a distribution onto some
>         empirical data,
>         and it does so even when I do not give the function the
>         initial point
>         in the form FindDistributionParameters[data,distribution,
>         {{param1,init1},{param2,init2},...}], but rather simply
>         FindDistributionParameters[data,distribution].  I would like
>         to know
>         how Mathematica initializes its search for parameters in the
>         latter
>         case.  Any insight would be greatly appreciated.
>
>
>     It varies by distribution. A few distributions have closed forms
>     for MLEs. In many cases method of moments estimates can be
>     obtained fairly quickly and these are used as starting values. In
>     other cases quantile-based estimates or estimates based on series
>     or other approximations are used. In cases where the default
>     parameter estimation is done via NMaximize, NMaximize's
>     initialization is used.
>
>     Darren Glosemeyer
>     Wolfram Research
>
>


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