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Re: FindDistributionParameters

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126676] Re: FindDistributionParameters
  • From: Darren Glosemeyer <darreng at wolfram.com>
  • Date: Wed, 30 May 2012 04:12:07 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201205290947.FAA06712@smc.vnet.net>

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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