I have a 2D uniform distribution. I would like to assign probability-weights in the distribution, according to the standard deviation to convert the distribution into a 2D gaussian.

I know how to do it in the 1D case, by splitting the points from -1 to 1 sigma, etc and assigning the probability as a weight but I haven't found a way to combine the probabilities from the 2 planes (eg at 1 sigma in x and 6 sigma in y)


The Gaussian distribution is separable. Apply your transformation to each coordinate separately and you will get a 2D Gaussian.

If $G(x)$ is a 1D Gaussian, then $G(x) G(y)$ is a 2D Gaussian.

Thus, transform the distribution first according to one coordinate, creating a distribution that has normal distribution in one direction and uniform in the other. Then transform it again according to the other coordinate.

  • $\begingroup$ A point between 0-1 sigma in x has Px=0.34 for a normal gaussian. The same point is in 2-3 sigma in y and has a Py = 0.02. How can I combine both probabilities and assign only one value to each point? $\endgroup$
    – Uno123
    Apr 9 '18 at 13:46
  • $\begingroup$ By multiplication. See the edit of the answer. $\endgroup$ Apr 9 '18 at 14:03

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.