Distance distribution to the closest point in a uniform distribution over the intersection of two circles

Maurilio Matracia

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Mar 30, 2021
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Hello,
I have a number N of points (represented as stars in the picture) distributed over the intersection of two horizontal circles C1(0,0,R1) and C2(0,U,R2), with R1>R2 and R1>U.
I am trying to determine what are the CDF and the PDF of the distribution of the distance to the closest point from an observer located in (0,U).
Do you have any suggestion or reference to recommend?

Thank you in advance,
Maurilio
 

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