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Module-1-Example-9.R
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Module-1-Example-9.R
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# The Skew-Normal and Related Distributions
# the following library can also be used to generate skewed data
# install.packages("sn")
# library(sn)
# rightSkewed <- rsn(n=10000, xi = 9, omega = 10, alpha = 7)
# leftSkewed <- rsn(n=10000, xi = 1, omega = 5, alpha = 1, tau = 1)
# we use beta distribution to generate skewed data
# set the random initial start as constant value
set.seed(1)
# generate 3 different data sets.
leftSkewed <- rbeta(4000,9,1.2)*40
rightSkewed <- rbeta(4000,1,9)*40
normalData<-rnorm(4000, mean = 20, sd=5)
# Begin with visualization.
######################################################
par(mfrow=c(1,3))
######################################################
hist(leftSkewed,
probability=T, nclass=max(leftSkewed)-min(leftSkewed)+1,
col='lightblue',
main='Left Skewed' , border = F)
lines(density(leftSkewed,bw=1), col='red', lwd=3)
# plot(density(leftSkewed), main='Left Skewed' , col='red', lwd=3, type="l")
abline(v=mean(leftSkewed), col='blue', lwd=3)
abline(v=median(leftSkewed), col='green', lwd=3)
text(mean(leftSkewed)+2, .19, "Mean", cex = 1.6, col='blue')
text(mean(leftSkewed)+2, .20, "Median", cex = 1.6, col='green')
######################################################
hist(normalData,
probability=T, nclass=max(normalData)-min(normalData)+1,
col='lightblue',
main='Normal', border = F)
lines(density(normalData,bw=1), col='red', lwd=3)
#plot(density(normalData), main='Normal' , col='red', lwd=3, type="l")
abline(v=mean(normalData), col='blue', lwd=3)
abline(v=median(normalData), col='green', lwd=3)
######################################################
hist(rightSkewed,
probability=T, nclass=max(rightSkewed)-min(rightSkewed)+1,
col='lightblue',
main='Right Skewed', border = F)
ines(density(rightSkewed,bw=1), col='red', lwd=3)
# plot(density(rightSkewed), main='Right Skewed' , col='red', lwd=3, type="l")
abline(v=mean(rightSkewed), col='blue', lwd=3)
abline(v=median(rightSkewed), col='green', lwd=3)
text(mean(rightSkewed)-3, .12, "Mean", cex = 1.6, col='blue')
text(mean(rightSkewed)-3, .13, "Median", cex = 1.6, col='green')
######################################################
# Optional Material - Skeweness tests
######################################################
# Some good reference to read about it
# https://en.wikipedia.org/wiki/Skewness
# https://help.gooddata.com/display/doc/Normality+Testing+-+Skewness+and+Kurtosis
# Test implementation in R
# https://www.r-bloggers.com/measures-of-skewness-and-kurtosis/
# One time installation of moments package is needed.
# install.packages("moments")
library(moments)
# SKEWNESS Test.
# As a general rule of thumb:
# If skewness is less than -1 or greater than 1, the distribution is highly skewed.
# If skewness is between -1 and -0.5 or between 0.5 and 1, the distribution is moderately skewed.
# If skewness is between -0.5 and 0.5, the distribution is approximately symmetric.
# KURTOSIS
# Kurtosis tells you the height and sharpness of the central peak, relative to that of a standard bell curve.
# Values for a right Skewed, Positive Skewed.
skewness(rightSkewed)
kurtosis(rightSkewed)
# Values for a left Skewed, Negative Skewed
skewness(leftSkewed)
kurtosis(leftSkewed)
# Values for a normal Skewed
skewness(normalData)
kurtosis(normalData)