# Below is R code for plotting normal distributions - illustrating
# the changes in the distribution when standard deviation changes.
# -selected graphics are imbedded below
#
# Also calculates area under the normal curve for given Z
#
# Finally plots 3-D bivariate normal density
#
#############################################
# PROGRAM NAME: NORMAL_PLOT_R
#
# ECON 206
#
# ORIGINAL SOURCE: The Standard Normal Distribution in R:
# http://msenux.redwoods.edu/math/R/StandardNormal.php
#
#
#
#
#PLOT NORMAL DENSISTY
x=seq(-4,4,length=200)
y=dnorm(x,mean=0,sd=1)
plot(x,y,type="l",lwd=2,col="red")
#######################################
###################################
# INCREASE THE STANDARD DEVIATION
x=seq(-4,4,length=200)
y=dnorm(x,mean=0,sd=2.5)
plot(x,y,type="l",lwd=2,col="red")
#####################################
####################################
# DECREASE THE STANDARD DEVIATION
x=seq(-4,4,length=200)
y=dnorm(x,mean=0,sd=.5)
plot(x,y,type="l",lwd=2,col="red")
# CALCULATING AREA FOR GIVEN Z-VALUES
# RECALL, FOR THE STANDARD NORMAL DISTRIBUTION THE MEAN = 0 AND
# THE STANDARD DEVIATION = 1
# THE pnorm FUNCTION GIVES THE PROBABILITY FOR THE AREA TO THE LEFT
# OF THE SPECIFIED Z-VALUE ( THE FIRST VALUE ENTERED IN THE FUNCTION)
# THE OUTPUT SHOULD MATCH WHAT YOU GET FROM THE NORMAL TABLE IN YOUR BOOK
# OR THE HANDOUT I SENT YOU
pnorm(0,mean=0, sd=1) # Z =0
pnorm(1,mean=0, sd=1) # Z <= 1
pnorm(1.55, mean=0, sd=1) # Z<=1.55
pnorm(1.645, mean=0, sd=1) # Z<= 1.645
# LETS LOOK AT A BIVARIATE NORMAL
# DISTRIBUTION
# first simulate a bivariate normal sample
library(MASS)
bivn <- mvrnorm(1000, mu = c(0, 0), Sigma = matrix(c(1, 0, 0, 1), 2))
# now we do a kernel density estimate
bivn.kde <- kde2d(bivn[,1], bivn[,2], n = 100)
# now plot your results
contour(bivn.kde)
image(bivn.kde)
persp(bivn.kde, phi = 45, theta = 30)
# fancy contour with image
image(bivn.kde); contour(bivn.kde, add = T)
# fancy perspective
persp(bivn.kde, phi = 45, theta = 30, shade = .1, border = NA)
###############################################
