MATLAB: How to plot distribution curves of two vectors

histogramstatistics

I have two vectors, charge 'q' and corresponding phase angle 'Ph', each of size 89905×1. 'Ph'- min=0 degree, max=360 degree & 'q'- min=-4e-12, max=4.5e-12. I want to plot distribution curves, in which the x-axis is my phase angle vector which is divided into small phase windows of width,say 1.5 degree and y axis : 1. number of charges present in that phase window. 2. sum of charge values observed in phase window. 3. average value of charge value observed in phase window. 4. maximum value of charge observed in phase window.

Best Answer

Use discretize to build your bins and accumarray for the statistics of each bin:

bins = 0:1.5:360;
binindex = discretize(Ph, bins);
binstarts = bins(1:end-1)'; %last bin includes both edges. See discretize doc
bincount = accumarray(binindex, q, size(binstarts), @numel); %number of charge per bin
binsum = accumarray(binindex, q, size(binstarts)); %sum of charge per bin (default function of accumarray)
binmean = accumarray(binindex, q, size(binstarts), @mean); %average of charge
binmax = accumarray(binindex, q, size(binstarts), @max); %max of charge
plot(binstarts, [bincount, binsum, binmean, binmax])

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MATLAB: How to get a random value in a matrix, given a probability of each value being chosen

Note that your probabilities should sum up to 1. Otherwise, they're not probabilities. So you need to divide them by the sum of column 2.

There are probably something in the Stats and Machine learning toolbox but, if like me, you don't have it, this would do:

M = [234.6591  0.4028
     416.1825  0.7144
     433.2481  0.7436
     566.2786  0.9720
     472.4878  0.8110
     582.1153  0.9992
     545.5523  0.9364
     565.2468  0.9702];
numsamples = 1000;  % however many you want
bins = [0; cumsum(M(:, 2)) / sum(M(:, 2))]; %create bins whose width is the probability

samples = M(discretize(rand(numsamples, 1), bins), 1);

You can easily check that the samples are generated according to your probability:

>>numsamples = 1e8;  
>>bins = [0; cumsum(M(:, 2)) / sum(M(:, 2))]; %create bins whose width is the probability
>>samples = M(discretize(rand(numsamples, 1), bins), 1);  %generate lots of samples
>>[~, idx] = ismember(samples, M(:, 1)); 
>>prob = accumarray(idx, 1) / numsamples;  %generate histogram of each sample
>>notaprob = prob * sum(M(:, 2))  %to convert back to your 'not probabilities' in column 2
notaprob =
    0.4029
    0.7146
    0.7436
    0.9721
    0.8109
    0.9992
    0.9364
    0.9699

MATLAB: How to write Continue Long Statements on Multiple Lines

Use repmat to avoid manually typing all 160 of those ‘%q’ repeats!

Try this:

formatSpec = ['%f',repmat('%q',1,160), '%[^\n\r]'];

Best Answer

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MATLAB: How to get a random value in a matrix, given a probability of each value being chosen

MATLAB: How to write Continue Long Statements on Multiple Lines

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