Examples of R-code

2016-04-11T20:33:36-04:00

Examples of R-code

Example: Covariance calculation by numerical double integral.

#First, install the package "cubature" with install.packages("cubature").
#You only need to do it once.

library(cubature) # load the package "cubature"
f <- function(x) { 6 * x[1] * (x[2] > x[1])} # This is the density, "x" is a 2D-vector

E.XY <- adaptIntegrate(function(x) x[1]*x[2]*f(x), lowerLimit = c(0, 0), 
                       upperLimit = c(1, 1))
E.X <- adaptIntegrate(function(x) x[1]*f(x), lowerLimit = c(0, 0), 
                      upperLimit = c(1, 1))
E.Y <- adaptIntegrate(function(x) x[2]*f(x), lowerLimit = c(0, 0), 
                      upperLimit = c(1, 1))

cov.XY <- E.XY$integral - E.X$integral * E.Y$integral #E.X, E.Y, E.XY have several fields like 
                                                      #E.X$integral E.X$error and so on. 
                                                      #We need only the integral field.
cov.XY

Examples of R-code

2016-03-05T15:40:31-04:00

Examples of R-code

Example: Approximation of the Gaussian distribution by sums of Bernoulli and uniform random variables.

#Generating data
repet <- 10000
size <- 100 
p <- .5
data <- (rbinom(repet, size, p) - size * p) / sqrt(size * p * (1-p))
hist(data, freq = FALSE)

#Histograms

#By default you get a frequency histogram. 
#To get a density you set "freq = FALSE".
#To control the number of bins use "breaks = ". 

hist(data, breaks = size/2, col = 'red', freq = FALSE)

#Plotting the pdf of the normal distribution

x <- seq(min(data) - 1, max(data) + 1, .01)
lines(x, dnorm(x), col='green', lwd = 4)
 
#similar exercise for uniform random variables.

size <- 3 
data <- runif(repet * size)
data.matrix  <- matrix(data, nrow = size)
mu <- size * 1/2
sigma <- sqrt(size * 1/12)
data <- (colSums(data.matrix) - mu )/ sigma
hist(data, breaks = 100, col = 'red', freq = FALSE)
lines(x, dnorm(x), col = 'green', lwd = 4)

Department of Mathematics and Statistics, Binghamton University people:kargin:math447

Examples of R-code

Examples of R-code

Example: Covariance calculation by numerical double integral.

Examples of R-code

Examples of R-code

Example: Approximation of the Gaussian distribution by sums of Bernoulli and uniform random variables.