Re: distribution fitting

• To: mathgroup at smc.vnet.net
• Subject: [mg90373] Re: [mg90343] distribution fitting
• From: mante <claude.mante at univmed.fr>
• Date: Tue, 8 Jul 2008 02:22:38 -0400 (EDT)
• References: <200807061120.HAA14716@smc.vnet.net>

```Youness Eaidgah wrote:
> Dear friends,
> I have a set of data and I want to fit a distribution on this data.I know
> that some software like Bestfit do this and also incorporate several tests
> like goodness-of-fit tests, c2 test, Kolmogorov-Smirnov test, and
> Anderson-Darling test, and finally parameter estimation. is it possible in
> Mathematica? can Mathematica find the most suitable distribution for a set
> of data? can it estimate the distribution parameters also? I really
> appreciate if you instruct me about this in Mathematica.
> Best regards,
> Tomas
>
>
>
There are few statistical packages in Mathematica (Hypothesis testing,
linear on nonlinear regression, statistical distributions, Clustering,
Multivarate statistics, ...) but you can easily fit distributions with
the available commands.

For instance, suppose you woul like to fit some chi-square distribution
(in the least-square sense):

(* Packages  *)
Needs["Statistics`ContinuousDistributions`"]
Needs["NonlinearRegression`"]

(*     A sample  *)
Dist = ChiSquareDistribution[5];
don = RandomReal[Dist, 100];

(*  Empirical distribution function  *)
QQ = Map[{#[[2]], #[[1]]} &, QuantileForm[don]];
ListPlot[QQ]

(* Estimate degrees of  freedom  *)
NonlinearRegress[QQ, CDF[ChiSquareDistribution[K], x], {K}, x]

Hope this helps,
Claude

--
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Claude Manté

UMR CNRS 6117 LMGEM
http://www.com.univ-mrs.fr/LMGEM/

Centre d'Océanologie de Marseille
Campus de Luminy, Case 901
13288 MARSEILLE Cedex 09
tel : (+33) 491 829 127
fax : (+33) 491 829 119

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```

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