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Re: Re: Gaussian PDF Overlay

• To: mathgroup at smc.vnet.net
• Subject: [mg19318] Re: [mg19283] Re: [mg19277] Gaussian PDF Overlay
• From: BobHanlon at aol.com
• Date: Sat, 14 Aug 1999 23:42:49 -0400
• Sender: owner-wri-mathgroup at wolfram.com

Lawrence,

I had a mistake in the scaling for my earlier reply. This is a corrected 
version, formatted as a function.

Needs["Statistics`ContinuousDistributions`"];
Needs["Statistics`DataManipulation`"];
Needs["Graphics`Graphics`"];
Needs["Utilities`FilterOptions`"];

Options[plotContDistData] = {nbrBins -> 10};

plotContDistData::usage = 
    "plotContDistData[dist, data] overlays the PDF for the specified \
continuous distribution over a bar chart of the data list.";

plotContDistData[dist_, data_List, opts___?OptionQ] := 
    Module[{mu, sigma, xmin, xmax, pltPDF, x, nbrVal = Length[data], step, k, 
        pltData, nBins, pltOpts},
      nBins = (nbrBins /. Flatten[{opts}]) /. Options[plotContDistData];
      pltOpts = FilterOptions[Plot, opts];
      mu = N[Mean[dist]];
      sigma = N[StandardDeviation[dist]];
      xmin = Max[mu - 3sigma, Domain[dist][[1, 1]]];
      xmax = Min[mu + 3sigma, Domain[dist][[1, 2]]];
      pltPDF = 
        Plot[PDF[dist, x], {x, xmin, xmax}, 
          PlotStyle -> AbsoluteThickness[2], DisplayFunction -> Identity, 
          Evaluate[pltOpts]];
      step = (xmax - xmin)/nBins;
      pltData = 
        GeneralizedBarChart[
          Transpose[{Table[xmin + step(k - 1/2), {k, nBins}], 
              BinCounts[data, {xmin, xmax, step}]/(step*nbrVal), 
              Table[step, {nBins}]}], DisplayFunction -> Identity, 
          Evaluate[pltOpts]];
      Show[{pltData, pltPDF}, DisplayFunction -> $DisplayFunction]];

Examples

dist = NormalDistribution[8, 2];
data = RandomArray[dist, 1000];
plotContDistData[dist, data, nbrBins -> 15];

dist = BetaDistribution[2, 2];
data = RandomArray[dist, 2000];
plotContDistData[dist, data, nbrBins -> 20];

dist = HalfNormalDistribution[5];
data = RandomArray[dist, 1000];
plotContDistData[dist, data];

dist = GammaDistribution[1, 5];
data = RandomArray[dist, 1000];
plotContDistData[dist, data];

Bob Hanlon

In a message dated 8/14/99 5:14:28 AM, BobHanlon at aol.com writes:

>Use a GeneralizedBarChart:
>
>Needs["Statistics`ContinuousDistributions`"]
>Needs["Statistics`DataManipulation`"];
>Needs["Graphics`Graphics`"];
>
>dist = NormalDistribution[mu = 4., sigma = 2.];
>
>xmin = mu - 3sigma; xmax = mu + 3sigma;
>
>plt1 = Plot[PDF[dist, x], {x, xmin, xmax}, PlotStyle -> AbsoluteThickness[2],
>
>      DisplayFunction -> Identity];
>
>nbrSamples = 1000;
>data = RandomArray[dist, nbrSamples];
>nbrBins = 10;
>step = (xmax - xmin)/nbrBins;
>freq = BinCounts[data, {xmin, xmax, step}]/nbrSamples;
>midPoints = Table[xmin + step(k - 1/2), {k, nbrBins}];
>
>plt2 = GeneralizedBarChart[Transpose[{midPoints, freq, Table[1, {nbrBins}]}],
>
>      DisplayFunction -> Identity];
>
>Show[{plt2, plt1}, DisplayFunction -> $DisplayFunction];
>