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Re: [S] How can I fit a t-distribution to a sample?

To: Bill Venables <Bill.Venables@cmis.csiro.au>
Subject: Re: [S] How can I fit a t-distribution to a sample?
From: Albyn Jones <jones@reed.edu>
Date: Wed, 31 May 2000 10:08:09 -0700 (PDT)
Cc: John.Gavin@ubsw.com, s-news@wubios.wustl.edu
In-reply-to: <3.0.32.20000531220540.01227230@pophost.nsw.cmis.csiro.au>
Sender: owner-s-news@wubios.wustl.edu
On Wed, 31 May 2000, Bill Venables wrote:

> 
> Your formula for the negative log-likelihood is incorrect and should be
> 
> ~ -log(dt((xx - mu)/sd, df)) + log(sd)
> 
> but I very much doubt that will solve the problem completely.  Once the df
> parameter of the t-distribution climbs above about 8 there is really very
> little shape difference in the t family so you will most likely need
> enormous samples to fix an estimate of it.

another idea is to reparametrize - for example map df by a smooth 
transformation the interval [0,1], where 1 corresponds to infinite df.  
Perhaps something like

              alpha = df/(c + df)

the constant c determines the df corresponding to alpha = .5.  This
won't alter the fact that you won't have good estimates of df for larger
df, but it might improve things both computationally and otherwise.

albyn

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