RinAction - R Functions - Probability Functions

gistfile1.r

#################################################
##             Probability  Functions          ##
#################################################

########################
# Normal Distribution 
#  - density (dnorm)
#  - distribution (pnorm)
#  - quantile (qnorm) 
#  - random deviate generation (rnorm)
########################

# standard normal curve on the interval [–3,3]
x <- pretty(c(-3,3), 30)
y <- dnorm(x)
plot(x, y,
     type = "l",
     xlab = "Normal Deviate",
     ylab = "Density",
     yaxs = "i"
     )
a <- pnorm(1.96)
a

# 90th percentile of a normal distribution with 
# a mean of 500 and a standard deviation of 100
p90 <- qnorm(.9, mean=500, sd=100)

# Generate 50 random normal deviates with a mean of
# 50 and a standard deviation of 10
ran50 <- rnorm(50, mean=50, sd=10)


################################
# Random NUmber Generation
################################

# Set the seed
runif(5)
runif(5) # should get different numbers

set.seed(1234)
runif(5)
set.seed(1234)
runif(5) # should get same numbers after setting the seed

#################################
# Multivariate Normal Data
#################################
#In simulation research and Monte Carlo studies, you often want to draw data from
#multivariate normal distribution with a given mean vector and covariance matrix.

library(MASS)
options(digits=3)
set.seed(1234)
mean <-c(230.7, 146.7, 3.6)
sigma <- matrix(c(15360.8, 6721.1,-47.1, 
                  6721.1, 4700.9, -16.5,
                  -47.1, -16.5, 0.3), nrow=3, ncol=3)

mydata <- mvrnorm(500, mean, sigma)
mydata <- as.data.frame(mydata)
names(mydata) <- c("y","x1","x2")

dim(mydata)
head(mydata, n=10)