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Re: FindDistributionParameters

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  • Subject: [mg126804] Re: FindDistributionParameters
  • From: Julian Haw <julianhaw at>
  • Date: Fri, 8 Jun 2012 03:37:43 -0400 (EDT)
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Ok.  So could you possibly give some insight on how NMaximize works?  Like
what routines would it use, and what initialization would it give to these
routines by default?

On Wed, Jun 6, 2012 at 6:11 PM, Darren Glosemeyer <darreng at>wrote:

>  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>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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