# Pdf for distance between two uniform random points in a circle

This is my first post in the group and I would be very thankful for any help. I am trying to develop a probability distribution for a performance analysis in my thesis. I am trying to look in to literature which provides the probability distribution for distance between two random points in a unit circle.

I would try to explain the problem. Suppose we have a point X and we have point x1 in the unit circle C1 which contains X. There is another unit circle X2 right next to the circle X1. There is a point x2 in the unit circle X2. Let d1 be the distance between X and x1 and d2 be the distance between X and x2. All the points are distributed within respective circles with random distribution. I want to know the probability distribution for d1/d2. Has anyone worked with a similar problem or anybody can direct me towards any literature.

Thank you so much for the help. Cheers, Waqas

• By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$? – Math1000 Nov 29 '15 at 9:01
• What are the centers of the circles? – Rodrigo de Azevedo Jun 28 '16 at 14:05

distance random points in circles

the first hit gives you the book: An introduction to geometrical probability by A.M. Mathai.

If you look into the book in Google preview, on page 217 you find a chapter treating your problem.

Maybe you can read it yourself ;-)!

Ciao

Karl

• Hi Karl. Thank you so much for the link. Unfortunately, the relevant chapter is not available for reading and I am unable to find it in library of my own uni. I hope I can get a similar book or this book to read through and get the solution. Thanks a lot for the help. – Waqas Sep 17 '14 at 7:18
• Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…> – Karl Sep 17 '14 at 7:25
• I have tried to open the link. It is probably from the german version of google but it says that from 77-555 it is not available for reading. I am trying to search it to suggest to my supervisor if I could buy it but I can not find any link as of yet to get it. I hope I can find the book as it clearly would help me a great deal. – Waqas Sep 17 '14 at 7:32
• Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps. – Karl Sep 17 '14 at 8:38
• Hi. I got the pages of the book from my library. The pdf involves an integral of which I am finding hard to solve. Could you help. I have posted the integral here – Waqas Sep 22 '14 at 4:11

Please look at this work 1 which has investigated the interference from neighbor cells, and hence, investigated the distribution of distances between users. Hope it works for you.