Generating random number from a pdf

Hi all,

I have bivariate probability density function f(x,y), which it doesn't follow any pdf from the known pdfs, and I would like to generate x, y random numbers that follow this pdf. Is there any way to do that in matlab?

Thanks in advance

Answer 1

[SK]

For simplicity, assume that the distribution has bounded support, i.e:

There is some Mx and My such that f(x,y) is zero for abs(x) > Mx and abs(y) > My.

One could probably do without this condition but it would a little more involved and in practice (unless you have a heavy-tailed distribution) it wont make much difference.

With this assumption, a general way to do it for any f(x,y) is as follows:

Let Mz = max(f(x,y)) over all x and y.

Now use rand to choose 3 numbers uniformly in the Box (-Mx < x < Mx) x (-My < y < My) x (z < Mz):

x = 2*Mx*(rand-0.5);

y = 2*My*(rand-0.5);

z = Mz*rand;

if z > f(x,y), reject x and y

otherwise add (x,y) to your set of generated points.

Best Regards,

Sandeep

[Symeon Mattes]

Thanks SK for your reply. This seem to work but because I have a huge amount of data and the grid is very dense is there any analytical method such as in 1D case, e.g. Using a sample PDF to generate random numbers ?