       Re: Fitting data

• To: mathgroup at smc.vnet.net
• Subject: [mg29594] Re: Fitting data
• From: Ignacio Rodriguez <ignacio at sgirmn.pluri.ucm.es>
• Date: Wed, 27 Jun 2001 05:12:28 -0400 (EDT)
• Organization: UCM
• References: <9h401r\$4a6\$1@smc.vnet.net> <9h8m2v\$qsi\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Try with the package Statistics`NonlinearFit

Richard wrote:

> An normal distibution wasn't a good example.
>
> What if I collected data from an experiment that I modeled by (for example):
>
> u(t)= a1 * sin(a2*t) + a3*exp(a4^3).
>
> How can I find a1, a2, a3 and a4 so that my function fits the data as good
> as possible?
>
> Thanx!!
>
> ----- Original Message -----
> From: <BobHanlon at aol.com>
To: mathgroup at smc.vnet.net
> Subject: [mg29594] Re: Fitting data
>
> >
> > In a message dated 2001/6/23 2:01:40 AM, wzn at jongnederland.nl writes:
> >
> > >How can I fit an function to data in mathematica? For example: in an
> > >experiment I collect data with a normal distrubution. I want to fit a
> normal
> > >curve to this data, with unknown mean and variance. Can I do this with
> > >the
> > >mean-squares-method or do I need an iterative algorithm or something like
> > >that?
> >
> > Fitting a distribution is not the same thing as fitting a function.
> >
> > For a normal distribution it is quite straightforward.  The maximum
> > likelihood
> > estimation of the mean of the distribution is Mean[data]
> >
> > The maximum likelihood estimation of the standard deviation of the
> > distribution is StandardDeviationMLE[data]
> >
> > Needs["Statistics`NormalDistribution`"];
> > Needs["Graphics`Colors`"];
> >
> > Let the "unknown" mean and standard deviation be
> >
> > {m, s} = {5*Random[], 2*Random[]}
> >
> > {1.3655769021908775, 0.2746217115738358}
> >
> > Taking a random sampling from this distribution
> >
> > data = RandomArray[NormalDistribution[m, s], {100}];
> >
> > The parameter estimates are then
> >
> > {me, se} = {Mean[data], StandardDeviationMLE[data]}
> >
> > {1.3879937672329135, 0.28629145363687175}
> >
> > Comparing the estimate of the distribution with the actual distribution
> >
> > Plot[{PDF[NormalDistribution[m, s], x], PDF[NormalDistribution[me, se],
> x],
> >       CDF[NormalDistribution[m, s], x],
> >       CDF[NormalDistribution[me, se], x]}, {x, m-2s, m+2s},
> >     PlotStyle -> {Blue, Red}, ImageSize -> 400];
> >
> >
> > Bob Hanlon
> > Chantilly, VA  USA
> >

--

Ignacio Rodriguez Ramirez de Arellano
Paseo Juan XXIII, 1

Tel. 34-91-394-3288
Fax  34-91-394-3245
e-mail: ignacio at sgirmn.pluri.ucm.es

```

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