# Ana Maria Popescu

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 Mar30 comment What is the distribution of the euclidean distance between two random points in 2d space? My understanding is, that given the problem above, by rotating the mean distance between A and B by the original angle θ, we will obtain 2 transformed Gaussian random variables (we use the Rotation matrix for the transformation). With these new RVs (one with non-zero mean and one with zero mean), of same variance, it is easy to demonstrate that the distribution of z is Rician (has been done in Mathematical Techniques for Engineers and Scientists). Mar29 awarded Teacher Mar29 comment What is the distribution of the euclidean distance between two random points in 2d space? Thank you for your answers! They have been useful to me. Took me a while to figure it out but I think I understood. Mar27 comment What is the distribution of the euclidean distance between two random points in 2d space? That may be so, but could you recommend a reference where this demonstration is made, for both RVs with non-zero means? In the reference that I mention in the post, there is such a demonstration but only for one non-zero mean RV. Mar27 comment What is the distribution of the euclidean distance between two random points in 2d space? It has been proven that z is Ricianly distributed only when X and Y are considered to be circular bivariate RVS -> X∼N(νcosθ,σ2) and Y∼N(νsinθ,σ2). In this case it can be considered that one of the points is set in the origin, but what I want to know is what happens when none of the points is set in the origin? Does the distribution remain Rician? Is it a generalized form and if so how would it look like? Mar27 comment What is the distribution of the euclidean distance between two random points in 2d space? The difference between this post and the previous thread (where I had my comment posted), is that the variance can be the same for the 2 RVs. Mar27 comment What is the distribution of the euclidean distance between two random points in 2d space? My question refers to the uncorrelated RVs, just as the previous post did. However, it is my understanding that the non-central chi-squared distribution is appropriate for z^2 not for z=sqrt(...). Maybe I am wrong, but even if I were to consider the noncentral chi distribution, instead of the chi-squared, it still does not make sense to me as the variable z does not have the expression of sqrt((xi/sigmai)^2) as here: en.wikipedia.org/wiki/Noncentral_chi_distribution Mar27 awarded Student Mar27 asked What is the distribution of the euclidean distance between two random points in 2d space? Mar26 awarded Editor