How to distribute random points according to the Epanechnikov distribution values

I want to get random points according to local maxima of the Epanechnikov distribution, such that the density of points is higher at the local maxima and the density of the points decreases in the minimum value.

[Star Strider]

Context — Generate random points inside a Epanechnikov distribution

Answer 1

[Roger Stafford]

(Correction: I have eliminated the 1) version of the preceding answer, since it was incorrect.)

I interpret your 2D Epanechnikov distribution for random points in the following way. Both x and y coordinates of the points have independent Epanechnikov distributions with respect to a center (x0,y0). The points are restricted to a square.

   x0 = 4; y0 = 6; % <-- Choose center of square
   L = 14; % <-- Choose length of square sides
   n = 8192; % <-- Choose number of points
   x = x0+(sin(asin(2*rand(1,n)-1)/3))*L;
   y = y0+(sin(asin(2*rand(1,n)-1)/3))*L;
   X = x0+[-1,1,1,-1,-1]*L/2;
   Y = y0+[-1,-1,1,1,-1]*L/2;
   plot(X,Y,'r-',x,y,'y.')
   axis equal

See https://www.mathworks.com/matlabcentral/answers/374276 for remarks about the method used to generate the Epanechnikov distribution.