       Re: Re: Fitting NormalDistribution to 2D List

• To: mathgroup at smc.vnet.net
• Subject: [mg31520] Re: [mg31459] Re: Fitting NormalDistribution to 2D List
• From: BobHanlon at aol.com
• Date: Thu, 8 Nov 2001 04:57:14 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```In a message dated 2001/11/7 8:25:33 AM, post_12 at hotmail.com writes:

>While the code you posted solves the specific example I asked about, I
>am still unable to fit my data to an arbitrary distribution (e.g.
>ExtremeValue, LaPlace). Is there a way to pass these distributions and
>my Tables of data to the Nonlinear fitting algorithm? Unrolling is
>unfortunately not an option; my machine (1GB RAM) ran out of memory
>trying to unroll 1 data set.
>

Needs["Statistics`ContinuousDistributions`"];
Needs["Statistics`DataManipulation`"];

binnedMean[data_]:=Tr[Times@@#&/@data]/Tr[data[[All,2]]];

dist = ExtremeValueDistribution[alpha, beta];

Generate random data

data = RandomArray[ExtremeValueDistribution[5,2],{10000}];

Bin the data

xmin = Min[data];
xmax = Max[data];
nbrBins = 20;

binnedData =
Select[({Mean[#], Length[#]}& /@
BinLists[data, {xmin, xmax, (xmax-xmin)/nbrBins}]), #[] > 0&];

Use binnedData statistics to estimate the parameters

m = binnedMean[binnedData];

{alphaEst, betaEst} = {alpha, beta} /. Solve[{Mean[dist] == m,
StandardDeviation[dist] ==
Sqrt[binnedMean[{(#[]-m)^2,#[]}&/@binnedData]]}, {alpha,
beta}][]

{5.024306536076431,
1.973745897321664}

Develop maximum likelihood estimates

logPDF[x_] :=
Evaluate[PowerExpand[Log[PDF[dist, x]]]];

logPDFprod = Simplify[Tr[#[]*logPDF[#[]]& /@ binnedData]];

eqns = {D[logPDFprod, alpha] == 0, D[logPDFprod, beta] == 0};

FindRoot[eqns, {alpha, alphaEst}, {beta, betaEst}]

{alpha -> 5.022912945470625,
beta -> 1.976571171905959}

Bob Hanlon
Chantilly, VA  USA

```

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