From: Kevin E. Thorpe <kevin.thorpe_at_utoronto.ca>

Date: Fri 13 May 2005 - 09:03:20 EST

Date: Fri 13 May 2005 - 09:03:20 EST

This thread was very timely for me since I will be teaching an introductory biostats course in the fall, including a session on CLT. I have shamelessly taken Dr. Venables' slick piece of code and wrapped it in a function so that I can vary the maximum sample size at will. I then created functions based on the first to sample from the exponential and the chi-squaredistributions. Lastly, I created a function to sample from a pdf with a parabolic shape (confirming in the process just how rusty my calculus is :-) ). My code is below for all to do with as they please.

Now, at the risk of asking a really obvious question ...

In my final function, I used the inverse probability integral transformation to sample from my parabolic distribution. I create a local function rparab shown here:

rparab <- function(nn) {

u <- 2*runif(nn) - 1

ifelse(u<0,-(abs(u)^(1/3)),u^(1/3))

}

It seems that in my version of R (2.0.1) on Linux, that calculating the cube
root of a negative number using ^(1/3) returns NaN. I looked at the help in
the arithmetic operators and did help.search("cube root"),
help.search("root")

and help.search("cube") and recognised no alternatives. So I used an
ifelse() to

deal with the negatives. Have I missed something really elementary?

Thanks

clt.unif <- function(n=20) {

N <- 10000

graphics.off()

par(mfrow = c(1,2), pty = "s")

for(k in 1:n) {

m <- (rowMeans(matrix(runif(N*k), N, k)) - 0.5)*sqrt(12*k)
hist(m, breaks = "FD", xlim = c(-4,4),

main = paste("Uniform(0,1), n = ",k,sep=""),
prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
pu <- par("usr")[1:2]

x <- seq(pu[1], pu[2], len = 500)

lines(x, dnorm(x), col = "red")

qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
abline(0, 1, col = "red")

Sys.sleep(1)

}

}

clt.exp <- function(n=20,theta=1) {

N <- 10000

graphics.off()

par(mfrow = c(1,2), pty = "s")

for(k in 1:n) {

m <- (rowMeans(matrix(rexp(N*k,1/theta), N, k)) - theta)/sqrt(theta^2/k)
hist(m, breaks = "FD", xlim = c(-4,4),

main = paste("exp(",theta,"), n = ",k,sep=""),
prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
pu <- par("usr")[1:2]

x <- seq(pu[1], pu[2], len = 500)

lines(x, dnorm(x), col = "red")

qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
abline(0, 1, col = "red")

Sys.sleep(1)

}

}

clt.chisq <- function(n=20,nu=1) {

N <- 10000

graphics.off()

par(mfrow = c(1,2), pty = "s")

for(k in 1:n) {

m <- (rowMeans(matrix(rchisq(N*k,nu), N, k)) - nu)/sqrt(2*nu/k)
hist(m, breaks = "FD", xlim = c(-4,4),

main = paste("Chi-Square(",nu,"), n = ",k,sep=""),
prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
pu <- par("usr")[1:2]

x <- seq(pu[1], pu[2], len = 500)

lines(x, dnorm(x), col = "red")

qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
abline(0, 1, col = "red")

Sys.sleep(1)

}

}

clt.parab <- function(n=20) {

rparab <- function(nn) {

u <- 2*runif(nn) - 1

ifelse(u<0,-(abs(u)^(1/3)),u^(1/3))

}

N <- 10000

graphics.off()

par(mfrow = c(1,2), pty = "s")

for(k in 1:n) {

m <- (rowMeans(matrix(rparab(N*k), N, k)))/sqrt(3/(5*k))
hist(m, breaks = "FD", xlim = c(-4,4),

main = paste("n = ",k,sep=""),

prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
pu <- par("usr")[1:2]

x <- seq(pu[1], pu[2], len = 500)

lines(x, dnorm(x), col = "red")

qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
abline(0, 1, col = "red")

Sys.sleep(1)

}

}

Bill.Venables@csiro.au wrote:

>Here's a bit of a refinement on Ted's first suggestion.

*>
**>
**> N <- 10000
**> graphics.off()
**> par(mfrow = c(1,2), pty = "s")
**> for(k in 1:20) {
**> m <- (rowMeans(matrix(runif(M*k), N, k)) - 0.5)*sqrt(12*k)
**> hist(m, breaks = "FD", xlim = c(-4,4), main = k,
**> prob = TRUE, ylim = c(0,0.5), col = "lemonchiffon")
**> pu <- par("usr")[1:2]
**> x <- seq(pu[1], pu[2], len = 500)
**> lines(x, dnorm(x), col = "red")
**> qqnorm(m, ylim = c(-4,4), xlim = c(-4,4), pch = ".", col = "blue")
**> abline(0, 1, col = "red")
**> Sys.sleep(1)
**> }
**>
**>
*

-- Kevin E. Thorpe Biostatistician/Trialist, Knowledge Translation Program Assistant Professor, Department of Public Health Sciences Faculty of Medicine, University of Toronto email: kevin.thorpe@utoronto.ca Tel: 416.946.8081 Fax: 416.971.2462 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Fri May 13 09:08:44 2005

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