Pdf for distance between two uniform random points in a circle












3












$begingroup$


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






circle uniform-distribution







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$?
    $endgroup$
    – Math1000
    Nov 29 '15 at 9:01






  • 1




    $begingroup$
    What are the centers of the circles?
    $endgroup$
    – Rodrigo de Azevedo
    Jun 28 '16 at 14:05
















3












$begingroup$


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






circle uniform-distribution







share|cite|improve this question









$endgroup$








  • 1




    $begingroup$
    By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$?
    $endgroup$
    – Math1000
    Nov 29 '15 at 9:01






  • 1




    $begingroup$
    What are the centers of the circles?
    $endgroup$
    – Rodrigo de Azevedo
    Jun 28 '16 at 14:05














3












3








3





$begingroup$


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






circle uniform-distribution







share|cite|improve this question









$endgroup$




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






circle uniform-distribution




circle uniform-distribution






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Sep 17 '14 at 5:55









WaqasWaqas

287




287








  • 1




    $begingroup$
    By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$?
    $endgroup$
    – Math1000
    Nov 29 '15 at 9:01






  • 1




    $begingroup$
    What are the centers of the circles?
    $endgroup$
    – Rodrigo de Azevedo
    Jun 28 '16 at 14:05














  • 1




    $begingroup$
    By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$?
    $endgroup$
    – Math1000
    Nov 29 '15 at 9:01






  • 1




    $begingroup$
    What are the centers of the circles?
    $endgroup$
    – Rodrigo de Azevedo
    Jun 28 '16 at 14:05








1




1




$begingroup$
By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$?
$endgroup$
– Math1000
Nov 29 '15 at 9:01




$begingroup$
By "the unit circle $C_1$ which contains $X$" do you mean that $X$ is the center of $C_1$?
$endgroup$
– Math1000
Nov 29 '15 at 9:01




1




1




$begingroup$
What are the centers of the circles?
$endgroup$
– Rodrigo de Azevedo
Jun 28 '16 at 14:05




$begingroup$
What are the centers of the circles?
$endgroup$
– Rodrigo de Azevedo
Jun 28 '16 at 14:05










2 Answers
2






active

oldest

votes


















0












$begingroup$

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






share|cite|improve this answer









$endgroup$













  • $begingroup$
    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.
    $endgroup$
    – Waqas
    Sep 17 '14 at 7:18










  • $begingroup$
    Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
    $endgroup$
    – Karl
    Sep 17 '14 at 7:25










  • $begingroup$
    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.
    $endgroup$
    – Waqas
    Sep 17 '14 at 7:32










  • $begingroup$
    Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
    $endgroup$
    – Karl
    Sep 17 '14 at 8:38












  • $begingroup$
    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
    $endgroup$
    – Waqas
    Sep 22 '14 at 4:11



















-2












$begingroup$

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.






share|cite|improve this answer











$endgroup$













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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    0












    $begingroup$

    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






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:18










    • $begingroup$
      Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
      $endgroup$
      – Karl
      Sep 17 '14 at 7:25










    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:32










    • $begingroup$
      Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
      $endgroup$
      – Karl
      Sep 17 '14 at 8:38












    • $begingroup$
      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
      $endgroup$
      – Waqas
      Sep 22 '14 at 4:11
















    0












    $begingroup$

    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






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:18










    • $begingroup$
      Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
      $endgroup$
      – Karl
      Sep 17 '14 at 7:25










    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:32










    • $begingroup$
      Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
      $endgroup$
      – Karl
      Sep 17 '14 at 8:38












    • $begingroup$
      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
      $endgroup$
      – Waqas
      Sep 22 '14 at 4:11














    0












    0








    0





    $begingroup$

    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






    share|cite|improve this answer









    $endgroup$



    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







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered Sep 17 '14 at 6:38









    KarlKarl

    6641614




    6641614












    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:18










    • $begingroup$
      Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
      $endgroup$
      – Karl
      Sep 17 '14 at 7:25










    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:32










    • $begingroup$
      Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
      $endgroup$
      – Karl
      Sep 17 '14 at 8:38












    • $begingroup$
      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
      $endgroup$
      – Waqas
      Sep 22 '14 at 4:11


















    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:18










    • $begingroup$
      Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
      $endgroup$
      – Karl
      Sep 17 '14 at 7:25










    • $begingroup$
      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.
      $endgroup$
      – Waqas
      Sep 17 '14 at 7:32










    • $begingroup$
      Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
      $endgroup$
      – Karl
      Sep 17 '14 at 8:38












    • $begingroup$
      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
      $endgroup$
      – Waqas
      Sep 22 '14 at 4:11
















    $begingroup$
    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.
    $endgroup$
    – Waqas
    Sep 17 '14 at 7:18




    $begingroup$
    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.
    $endgroup$
    – Waqas
    Sep 17 '14 at 7:18












    $begingroup$
    Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
    $endgroup$
    – Karl
    Sep 17 '14 at 7:25




    $begingroup$
    Hi Waqas, did you try this link, there is page 217-9:<books.google.de/…>
    $endgroup$
    – Karl
    Sep 17 '14 at 7:25












    $begingroup$
    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.
    $endgroup$
    – Waqas
    Sep 17 '14 at 7:32




    $begingroup$
    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.
    $endgroup$
    – Waqas
    Sep 17 '14 at 7:32












    $begingroup$
    Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
    $endgroup$
    – Karl
    Sep 17 '14 at 8:38






    $begingroup$
    Sorry that it doesn't work. Amazon gives also a preview, not these pages, but at least the bibliography. Maybe this helps.
    $endgroup$
    – Karl
    Sep 17 '14 at 8:38














    $begingroup$
    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
    $endgroup$
    – Waqas
    Sep 22 '14 at 4:11




    $begingroup$
    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
    $endgroup$
    – Waqas
    Sep 22 '14 at 4:11











    -2












    $begingroup$

    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.






    share|cite|improve this answer











    $endgroup$


















      -2












      $begingroup$

      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.






      share|cite|improve this answer











      $endgroup$
















        -2












        -2








        -2





        $begingroup$

        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.






        share|cite|improve this answer











        $endgroup$



        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.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Jun 28 '16 at 13:54

























        answered Jun 28 '16 at 11:42









        user76648user76648

        13




        13






























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            .mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output .infobox.bordered .mergedrow td,.mw-parser-output .infobox.bordered .mergedrow th{border:0;border-right:1px solid ...
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