R version 2.9.0 (2009-04-17)
Copyright (C) 2009 The R Foundation for Statistical Computing
ISBN 3-900051-07-0

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>  # gnbxml.r                November 2007
>  #
>  # generate normal random variable via Box-Muller method
>  #
>   set.seed(5151917)
>  #
>   N <- 1000         # how many to do
>  #
>   U <- runif(N)
>   V <- runif(N)
>   X <- cos(2*pi*U)*sqrt(-2*log(V))
>   Y <- sin(2*pi*U)*sqrt(-2*log(V))      # note reverse roles
>  # some simple analysis
>   XY <- t(rbind(X,Y))          # get right shape
>  # one way
>   mean(XY)
[1] 0.04549968
>  # second way
>   apply(XY,2,mean)
         X          Y 
0.05509137 0.03590799 
>  # one way
>   cov(XY)
            X           Y
X  0.90163753 -0.02383551
Y -0.02383551  0.90987914
>  # second way
>   apply(XY,2,var)
        X         Y 
0.9016375 0.9098791 
>  # third way
>   C <- var(XY)
>   C
            X           Y
X  0.90163753 -0.02383551
Y -0.02383551  0.90987914
>  # test whether X and Y are correlated
>   r <- C[1,2]/sqrt(C[1,1]*C[2,2])
>   t <- r*sqrt(N/(1-r*r))
>   c(r,t)
[1] -0.0263158 -0.8324670
>  #
>  # analyze X's then Y's using Kolmogorov-Smirnov & Anderson-Darling
>  #
>   sX <- sort(X)
>   w <- (2*(1:N)-1)/N
>  # first K-S
>   f <- pnorm(sX)
>   Dnm <- max(f-((1:N)-1)/N)   # Dn-
>   Dnp <- max((1:N)/N-f)       # Dn+
>   c(Dnp,Dnm)                  # print them
[1] 0.01144788 0.03855941
>   sqrt(N)*max(Dnp,Dnm)        # standardized statistic
[1] 1.219356
>  # now A-D
>   w <- (2*(1:N)-1)/N
>   lf <- pnorm(sX,log.p=TRUE)
>  #              reverse the order
>   lomf <- pnorm(rev(sX),lower.tail=F,log.p=TRUE)
>   A2X <- -N - sum(w*(lf+lomf))
>   A2X
[1] 2.284703
>  #                  repeat for Y 
>   sY <- sort(Y)
>  # first K-S
>   f <- pnorm(sY)
>   Dnm <- max(f-((1:N)-1)/N)   # Dn-
>   Dnp <- max((1:N)/N-f)       # Dn+
>   c(Dnp,Dnm)                  # print them
[1] 0.008809552 0.034118552
>   sqrt(N)*max(Dnp,Dnm)        # standardized statistic
[1] 1.078923
>  # now A-D
>   lf <- pnorm(sY,log.p=TRUE)
>  #              reverse the order
>   lomf <- pnorm(rev(sY),lower.tail=F,log.p=TRUE)
>   A2Y <- -N - sum(w*(lf+lomf))
>   A2Y
[1] 1.371618
>  # done
>   rm(list=ls())
>  q()