- #1

architect

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I have a problem in understanding how to bound a Gaussian distribution. LEt me describe the problem at hand: Let's say that we have a Gaussian distribution in the x-coordinate and a Gaussian distribution in the y-coordinate. Further, assume that the independent random variables x and y are defined from -infty to +infty. Therefore, if one finds the product of the marginal densities of x and y, the resultant joint distribution will have infinite support. If then one converts to the polar coordinate system so that x, y becomes r, phi it will imply directly that r is defined from 0 to infty.

This is what I am trying to avoid. I would like to define this distribution such that the random variable r is is lower bounded by some value, say r_min. In this respect, I would like to define x, y such that

[itex]x^2 + y^2 > r_{min}^2[/itex],

where [itex]r_{min}[/itex] denotes the minimum distance. I imagine this being a circular cap inside which the probability of finding a point is 0 and beyond which the random variable r is defined (and properly normalized).

My question essentially boils down to this. How does one achieve this? Is it by truncating the normal distribution (left truncation)?

Thanks in advance.

BR,

Alex