Pdf for distance between two uniform random points in a circle
$begingroup$
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
asked Sep 17 '14 at 5:55
WaqasWaqas
287
$endgroup$
add a comment |
$begingroup$
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
asked Sep 17 '14 at 5:55
WaqasWaqas
287
$endgroup$
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
add a comment |
$begingroup$
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
asked Sep 17 '14 at 5:55
WaqasWaqas
287
$endgroup$
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
asked Sep 17 '14 at 5:55
WaqasWaqas
287
asked Sep 17 '14 at 5:55
WaqasWaqas
287
asked Sep 17 '14 at 5:55
WaqasWaqas
287
asked Sep 17 '14 at 5:55
WaqasWaqas
287
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
add a comment |
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
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
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
answered Sep 17 '14 at 6:38
KarlKarl
6641614
$endgroup$
$begingroup$
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
|
show 2 more comments
$begingroup$
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.
answered Jun 28 '16 at 11:42
user76648user76648
13
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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
answered Sep 17 '14 at 6:38
KarlKarl
6641614
$endgroup$
$begingroup$
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
|
show 2 more comments
$begingroup$
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
answered Sep 17 '14 at 6:38
KarlKarl
6641614
$endgroup$
$begingroup$
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
|
show 2 more comments
$begingroup$
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
answered Sep 17 '14 at 6:38
KarlKarl
6641614
$endgroup$
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
answered Sep 17 '14 at 6:38
KarlKarl
6641614
answered Sep 17 '14 at 6:38
KarlKarl
6641614
answered Sep 17 '14 at 6:38
KarlKarl
6641614
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
|
show 2 more comments
$begingroup$
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
|
show 2 more comments
$begingroup$
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.
answered Jun 28 '16 at 11:42
user76648user76648
13
$endgroup$
add a comment |
$begingroup$
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.
answered Jun 28 '16 at 11:42
user76648user76648
13
$endgroup$
add a comment |
$begingroup$
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.
answered Jun 28 '16 at 11:42
user76648user76648
13
$endgroup$
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.
answered Jun 28 '16 at 11:42
user76648user76648
13
edited Jun 28 '16 at 13:54
answered Jun 28 '16 at 11:42
user76648user76648
13
answered Jun 28 '16 at 11:42
user76648user76648
13
answered Jun 28 '16 at 11:42
user76648user76648
13
13
add a comment |
add a comment |
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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