MATLAB: Discrete joint probability distribution

bivariatediscretejoint probability distributionMATLAB

I want to build the discrete joint probability distribution for two set of data. data are two groups of random numbers (wind speed) and (wind direction degree). the final results must be like table below.

Pij in the Table are numbers (probability values).

Which function should I use to do this?

Best Answer

You need to compute the histogram count for every pair (theta_i, v_j), and then normalize it by the sample size. Thus, histcounts2 will help.

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MATLAB: Making a contour plot from x and y data

The bivariate density can be computed using histcounts2. You'll need to specify either the number of bins or the bin edges for the x and y variables using one of the syntaxes below.

Here's what the solution will look like. xy is your nx2 matrix of [x,y] values.

[N,Xedges,Yedges] = histcounts2(xy(:,1), xy(:,2), 5);
% or use [N,Xedges,Yedges] = histcounts2(X,Y,Xedges,Yedges);
% Compute bin centers
Xcnt = Xedges(2:end) - abs(diff(Xedges(1:2))/2); 
Ycnt = Yedges(2:end) - abs(diff(Yedges(1:2))/2); 
figure()
contour(Xcnt,Ycnt, N)
% show bins
xlim = [min(Xedges),max(Xedges)]; 
ylim = [min(Yedges),max(Yedges)]; 
arrayfun(@(x)xline(x,'Color',[.8 .8 .8]),Xedges)
arrayfun(@(y)yline(y,'Color',[.8 .8 .8]),Yedges)
% colorbar
cb = colorbar(); 
ylabel(cb,'density')

MATLAB: Find bandwidth of Kernel Density Estimator

findpeaks

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MATLAB: Making a contour plot from x and y data

MATLAB: Find bandwidth of Kernel Density Estimator

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