[IPSUR-commits] r121 - in pkg/IPSUR: R man
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Tue Jan 5 14:35:08 CET 2010
Author: gkerns
Date: 2010-01-05 14:35:08 +0100 (Tue, 05 Jan 2010)
New Revision: 121
Removed:
pkg/IPSUR/R/clt.R
pkg/IPSUR/man/clt.Rd
Log:
will put them right back
Deleted: pkg/IPSUR/R/clt.R
===================================================================
--- pkg/IPSUR/R/clt.R 2010-01-05 13:29:33 UTC (rev 120)
+++ pkg/IPSUR/R/clt.R 2010-01-05 13:35:08 UTC (rev 121)
@@ -1,311 +0,0 @@
-##################################################
-# The Central Limit Theorem
-# want to investigate how the distribution of
-# x-bar changes as the sample size gets large
-
-population <- "rt" # pop'n distribution is Student's t
-r <- 3 # degrees of freedom parameter
-
-sample.size <- 2 # sample size
-
-N.iter <- 100000 # number of simulated xbar's
-
-
-clt1 <- function(population = "rt",
- r = 3,
- sample.size = 2,
- N.iter = 100000){
-
-#################################################################
-# initialize variables
-population <- get(population, mode = "function")
-xbar <- rep(0, N.iter)
-graphics.off()
-
-curve( dt(x, df = r ),
- xlim = c(-5,5),
- xlab = "Support Set",
- ylab = "Density",
- lwd = 2,
- main = "The Population Distribution \n (while we're waiting)" )
-abline( h = 0 , col = "grey" )
-
-
-########################################
-# Label the plot with mu
-text( 5,
- dt(0, df = r )*0.9,
- bquote( mu ==.(0) ),
- cex = 1.5,
- pos = 2 )
-
-# Label the plot with sigma^2
-text( 5,
- dt(0, df = r )*0.8,
- bquote( sigma^2 ==.(r/(r-2)) ),
- cex = 1.5,
- pos = 2 )
-
-
-#################################################
-# simulate xbar's
-
-xbar <- rowMeans( matrix(population(sample.size * N.iter, df = r),
- nrow = N.iter)
- )
-
-# Find mean and variance of xbar
-xbar.mean <- round( mean( xbar ), 4)
-xbar.var <- round( var( xbar ), 4)
-
-# window for graph
-low <- xbar.mean - 3*sqrt(xbar.var)
-up <- xbar.mean + 3*sqrt(xbar.var)
-
-dev.new()
-dev.set(3)
-# Draw histogram of simulated x-bars
-hist( xbar,
- breaks = 280,
- xlim = c(low,up),
- xlab = "",
- prob = TRUE,
- main = "Sampling Distribution of X-bar",
- sub = "Click to see Limiting Normal Density (in red)")
-
-########################################
-# Label the histogram with mean(xbar)
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar)),
- bquote( mean(xbar)==.(xbar.mean) ),
- cex = 1,
- pos = 2 )
-
-# Label the histogram with var(xbar)
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar))*0.9,
- bquote( var(xbar) ==.(xbar.var) ),
- cex = 1,
- pos = 2 )
-
-# Label the histogram with n
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar))*0.8,
- bquote( n ==.(sample.size) ),
- cex = 1.85,
- pos = 2 )
-
-######################################
-# Draw limiting Normal curve
-z <- locator( n = 1 )
-curve( dnorm(x, mean = xbar.mean, sd = sd(xbar)),
- lwd = 2,
- col = "red",
- add = T )
-}
-
-
-
-
-
-
-
-clt2 <- function(population = "runif",
- a = 0,
- b = 10,
- sample.size = 2,
- N.iter = 100000){
-
-#################################################################
-# initialize variables
-population <- get(population, mode = "function")
-xbar <- rep(0, N.iter)
-graphics.off()
-
-curve( dunif(x, min = a, max = b ),
- xlim = c(a-1,b+1), ylim = c(0, 1.3/(b-a)),
- xlab = "Support Set",
- ylab = "Density",
- lwd = 2,
- main = "The Population Distribution \n (while we're waiting)" )
-abline( h = 0 , col = "grey" )
-
-
-########################################
-# Label the plot with mu
-text( (a+b)/2,
- 0.9/(b-a),
- bquote( mu ==.((a+b)/2) ),
- cex = 1.5,
- pos = 1 )
-
-# Label the plot with sigma^2
-text( (a+b)/2,
- 0.8/(b-a),
- bquote( sigma^2 ==.( (b-a)^2/12 ) ),
- cex = 1.5,
- pos = 1 )
-
-
-#############################################
-# simulate xbar's
-xbar <-rowMeans(matrix(population(sample.size * N.iter, min = a, max = b),
- nrow = N.iter)
- )
-
-# Find mean and variance of xbar
-xbar.mean <- round( mean( xbar ), 4)
-xbar.var <- round( var( xbar ), 4)
-
-# window for graph
-low <- xbar.mean - 3*sqrt(xbar.var)
-up <- xbar.mean + 3*sqrt(xbar.var)
-
-dev.new()
-dev.set(3)
-# Draw histogram of simulated x-bars
-hist( xbar,
- breaks = 80,
- xlim = c(low,up),
- xlab = "",
- prob = TRUE,
- main = "Sampling Distribution of X-bar",
- sub = "Click to see Limiting Normal Density (in red)")
-
-########################################
-# Label the histogram with mean(xbar)
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar)),
- bquote( mean(xbar)==.(xbar.mean) ),
- cex = 1,
- pos = 2 )
-
-# Label the histogram with var(xbar)
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar))*0.9,
- bquote( var(xbar)==.(xbar.var) ),
- cex = 1,
- pos = 2 )
-
-# Label the histogram with n
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar))*0.8,
- bquote( n ==.(sample.size) ),
- cex = 1.85,
- pos = 2 )
-
-######################################
-# Draw limiting Normal curve
-z <- locator( n = 1 )
-curve( dnorm(x, mean = xbar.mean, sd = sd(xbar)),
- lwd = 2,
- col = "red",
- add = T )
-}
-
-
-clt3 <- function(population = "rgamma",
- alpha = 1.21,
- theta = 2.37,
- sample.size = 2,
- N.iter = 100000){
-
-#################################################################
-# initialize variables
-population <- get(population, mode = "function")
-xbar <- rep(0, N.iter)
-graphics.off()
-
-
-curve( dgamma(x, shape = alpha, scale = theta ),
- xlim = c(0, alpha*theta*(1 + 3*theta)),
- xlab = "Support Set",
- ylab = "Density",
- lwd = 2,
- main = "The Population Distribution \n (while we're waiting)" )
-abline( h = 0 , col = "grey" )
-
-f = function(x){dgamma(x, shape = alpha, scale = theta )}
-
-OPT = optimize( f,
- interval = c(0, alpha*theta*(1 + 3*theta)),
- maximum = TRUE)
-
-########################################
-# Label the plot with mu
-text( alpha*theta*(1 + 2*theta),
- (OPT$objective)*0.9,
- bquote( mu ==.(alpha*theta )),
- cex = 1.5,
- pos = 1 )
-
-# Label the plot with sigma^2
-text( alpha*theta*(1 + 2*theta),
- (OPT$objective)*0.8,
- bquote( sigma^2 ==.( alpha*theta^2 ) ),
- cex = 1.5,
- pos = 1 )
-
-
-#############################################
-# simulate xbar's
-xbar <- rowMeans(matrix(population(sample.size * N.iter, shape = alpha, scale = theta),
- nrow = N.iter)
- )
-
-# Find mean and variance of xbar
-xbar.mean <- round( mean( xbar ), 4)
-xbar.var <- round( var( xbar ), 4)
-
-# window for graph
-low <- xbar.mean - 3*sqrt(xbar.var)
-up <- xbar.mean + 3*sqrt(xbar.var)
-
-dev.new()
-dev.set(3)
-# Draw histogram of simulated x-bars
-hist( xbar,
- breaks = 80,
- xlim = c(low,up),
- xlab = "",
- prob = TRUE,
- main = "Sampling Distribution of X-bar",
- sub = "Click to see Limiting Normal Density (in red)")
-
-########################################
-# Label the histogram with mean(xbar)
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar)),
- bquote( mean(xbar)==.(xbar.mean) ),
- cex = 1,
- pos = 2 )
-
-# Label the histogram with var(xbar)
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar))*0.9,
- bquote( var(xbar)==.(xbar.var) ),
- cex = 1,
- pos = 2 )
-
-# Label the histogram with n
-text( up,
- dnorm(xbar.mean, mean = xbar.mean, sd = sd(xbar))*0.8,
- bquote( n ==.(sample.size) ),
- cex = 1.85,
- pos = 2 )
-
-######################################
-# Draw limiting Normal curve
-z = locator( n = 1 )
-curve( dnorm(x, mean = xbar.mean, sd = sd(xbar)),
- lwd = 2,
- col = "red",
- add = T )
-
-}
-
-
-
-
-
-
Deleted: pkg/IPSUR/man/clt.Rd
===================================================================
--- pkg/IPSUR/man/clt.Rd 2010-01-05 13:29:33 UTC (rev 120)
+++ pkg/IPSUR/man/clt.Rd 2010-01-05 13:35:08 UTC (rev 121)
@@ -1,38 +0,0 @@
-\name{The Central Limit Theorem}
-\alias{The Central Limit Theorem}
-\alias{clt1}
-\alias{clt2}
-\alias{clt3}
-
-\title{Investigating the Central Limit Theorem}
-\description{
- These functions were written for students to investigate the Central Limit Theorem. For more information, see the exercises at the end of the chapter "Sampling Distributions" in IPSUR.
-}
-
-\usage{
-clt1(population = "rt", r = 3, sample.size = 2, N.iter = 100000)
-clt2(population = "runif", a = 0, b = 10, sample.size = 2, N.iter = 100000)
-clt3(population = "rgamma", alpha = 1.21, theta = 2.37, sample.size = 2, N.iter = 100000)
-}
-
-\arguments{
- \item{population}{the name of a population distribution, in its random generator form.}
- \item{sample.size}{the sample size.}
- \item{N.iter}{the number of samples desired.}
- \item{r}{the degrees of freedom for Student's t distribution.}
- \item{a}{the minimum value of a continuous uniform distribution.}
- \item{b}{the maximum value of a continuous uniform distribution.}
- \item{alpha}{the shape parameter of a gamma distribution.}
- \item{theta}{the scale parameter of a gamma distribution.}
-}
-
-\details{
- When the functions are called a plot window opens to show a graph of the PDF of the population distribution. On the display are shown numerical values of the population mean and variance. The computer simulates random samples of size \code{sample.size} from the distribution a total of
-\code{N.iter} times, and sample means are calculated for each sample. Next follows a histogram of the simulated sample means, which closely approximates the sampling distribution of the sample mean.
-Also shown are the sample mean and sample variance of all of the simulated sample means. As a final step, when the user clicks the second plot, a normal curve with the same mean and variance as the simulated sample means is superimposed over the histogram.
-}
-
-
-\author{G. Jay Kerns \email{gkerns at ysu.edu}}
-
-\keyword{misc}
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