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
Where is your problem? Google is your friend!
If you google the words:
distance random points in circles
the first hit gives you the book: An introduction to geometrical probability by A.M. Mathai.
To find in Google:
http://books.google.de/books/about/An_Introduction_to_Geometrical_Probabili.html?id=FV6XncZgfcwC&redir_esc=y
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