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Visualize Central Limit Theorem in Array Plot

Display a Uniform Distribution

This example shows how to use and configure the dsp.ArrayPlot to visualize the Central Limit Theorem. This theorem states that the mean of a large number of independent random variables with finite mean and variance exhibits a normal distribution.

First, generate uniformly distributed random variables in MATLAB® using the rand function. Find their distributions using the hist function. At the MATLAB command line, type:

numsamples  = 1e4;
numbins     = 20;
r = rand(numsamples,1);
hst = hist(r,numbins);

Create a new Array Plot object.

hap3 = dsp.ArrayPlot;

Configure the properties of the Array Plot object to plot a histogram.

hap3 = dsp.ArrayPlot;
hap3.XOffset = 0;
hap3.SampleIncrement = 1/numbins;
hap3.PlotType = 'Stem';
hap3.YLimits = [0, max(hst)+1];

Call the step method to plot the uniform distribution.

step(hap3,hst');

The following Array Plot figure appears, showing a uniform distribution.

Display the Sum of Many Uniform Distributions

Next, calculate the mean of multiple uniformly distributed random variables. As the number of random variables increases, the distribution more closely resembles a normal curve. Run the release method to let property values and input characteristics change. At the MATLAB command line, type:

release(hap3);

Change the configuration of the Array Plot properties for the display of a distribution function.

numbins    = 201;
numtrials  = 100;
r = zeros(numsamples,1);
hap3.SampleIncrement = 1/numbins;
hap3.PlotType = 'Stairs';

Call the step method repeatedly to plot the uniform distribution.

for ii = 1:numtrials
    r = rand(numsamples,1)+r;
    hst = hist(r/ii,0:1/numbins:1);
    hap3.YLimits = [min(hst)-1, max(hst)+1];
    step(hap3,hst');
    pause(0.1);
end

When the simulation has finished, the Array Plot figure displays a bell curve, indicating a distribution that is close to normal.

Inspect Your Data by Zooming

The zoom tools allow you to zoom in simultaneously in the directions of both the x- and y-axes or in either direction individually. For example, to zoom in on the distribution between 0.3 and 0.7, you can use the Zoom X option.

  • To activate the Zoom X tool, select Tools > Zoom X, or press the corresponding toolbar button ( ). You can determine if the Zoom X tool is active by looking for an indented toolbar button or a check mark next to the Tools > Zoom X menu option.

  • Next, zoom in on the region between 0.3 and 0.7. In the Array Plot window, click on the 0.3-second mark, and drag to the 0.7-second mark. The display reflects this new x-axis setting, as shown in the following figure.

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