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Re: FindDistributionParameters

• To: mathgroup at smc.vnet.net
• Subject: [mg126805] Re: FindDistributionParameters
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Fri, 8 Jun 2012 03:38:04 -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> <4FCFD599.1090007@wolfram.com> <CAKYgLuveeLXLzBP3ULUJcoN+j0M5ccynYeH=ZMS37=nXP1M64Q@mail.gmail.com>

Sure. If you type NMaximize into the Documentation Center (on the Help 
menu) that will give general information about the function with several 
examples. There are also some tutorials that give a bit more detail, 
which you can access by entering

tutorial/ConstrainedOptimizationOverview

or

tutorial/ConstrainedOptimizationGlobalNumerical

in the Documentation Center. The first will lead to lots of 
documentation about constrained optimization. The second speaks more 
specifically about NMinimize and its options and methods. NMaximize uses 
the same options and methods as NMinimize to solve the maximization 
problem instead of the minimization problem.

Darren Glosemeyer
Wolfram Research

On 6/7/2012 9:20 AM, Julian Haw wrote:
> 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 wolfram.com 
> <mailto:darreng at wolfram.com>> 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 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
>>
>>
>
>