1

I have two different 2D Homogeneous Poisson Point Processes $Λ_1$ and $Λ_2$ with densities $λ_1$ and $λ_2$. The PDF of the distance of the nearest point to the origin $(0,0)$ for each HPPP is known

$f_{R_1}(r)=2πλ_1re^{(-λ_1πr^2)}$, $f_{R_2}(r)=2πλ_2re^{(-λ_2πr^2)}$

If $R_1$ is the random variable of the distance between the origin and the nearest point to the origin of $Λ_1$ and $R_2$ is the random variable of the distance between the origin and the nearest point to the origin of $Λ_2$, I am interested in finding the PDF of the distance between these two points (that belong to different HPPPs).

billy
  • 23
  • Con you find the distribution of the position (rather than distance) of the nearest point to the origin of $\Lambda_1$? Similarly $\Lambda_2$? And their difference? And then the distance involved? – Henry Mar 10 '22 at 14:30

0 Answers0