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question on runif

5 messages · Wolfgang Amadeus, Alfredo, (Ted Harding) +1 more

Alfredo
# 
ang<-runif(20,0,2*pi)
x<-cos(ang) +0.4
y<-sin(ang) +0.8

plot(x,y,ylim=c(-3,3),xlim=c(-3,3))

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Wolfgang?Amadeus
Sent: Wednesday, January 20, 2010 5:26 AM
To: r-help
Subject: [R] question on runif

Hello! 
I have a question on uniform distribution. 
 I want to plot n, say 20, points, uniformly distributed, in a circle, with
radius=0.1 and center,say, (0.4, 0.8)
I do not know how~ 
 Thank you for your time.
 Yours 
Wolfgang Amadeus


______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Alfredo
# 
Oops forgot to include the radius

ang<-runif(200,0,2*pi)
x<-cos(ang)*.1 +0.4
y<-sin(ang)*.1 +0.8

plot(x,y)

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Wolfgang?Amadeus
Sent: Wednesday, January 20, 2010 5:26 AM
To: r-help
Subject: [R] question on runif

Hello! 
I have a question on uniform distribution. 
 I want to plot n, say 20, points, uniformly distributed, in a circle, with
radius=0.1 and center,say, (0.4, 0.8)
I do not know how~ 
 Thank you for your time.
 Yours 
Wolfgang Amadeus


______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
(Ted Harding)
# 
Alfredo's solution will provide n (=200 in his case) points
uniformly distributed along the *circumference* of the circle.
Wolfgang_Amadeus(!), you wanted them "*in* a circle".

If what you mean is "uniformly distributed over the area within
the circle", then you also need to generate the radii at random.

If P, with polar coordinates (r,t), is uniformly distributed
over the internal area of a circle with radius R and centre (0,0),
then the angle t is uniformly distributed over (0,2*pi) as in
Alfredo's solution, and the density of r is 2*(r/R^2) and the
CDF of r is (r/R)^2.

If U is uniformly distributed on (0,1), then Y = sqrt(U) has
the CDF y^2, since
  P(Y < y) = P(sqrt(U) < y) = P(U < y^2) = y^2.

Hence:

  r0 <- 0.1
  X0 <- 0.4
  Y0 <- 0.8
  n  <- 200
  r  <- r0*sqrt(runif(n))
  t  <- 2*pi*runif(n)
  X  <- X0 + r*cos(t)
  Y  <- Y0 + r*sin(t)
  plot(X,Y)

Ted.
On 20-Jan-10 11:31:49, Alfredo wrote:
--------------------------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
Fax-to-email: +44 (0)870 094 0861
Date: 20-Jan-10                                       Time: 12:16:05
------------------------------ XFMail ------------------------------
Rolf Turner
# 
Ted, Alfredo, et al:  Please stop doing this <expletive deleted>
jerk's homework for him!!!

	cheers,

		Rolf Turner

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