Load the Iris dataset into the df variable:

df<-iris

Select rows corresponding to the setosa species only:

df=df[df$Species=='setosa',]

Import the kdensity library:

library(kdensity)

Calculate and plot the KDE from the kdensity function for sepal length:

dist <- kdensity(df$Sepal.Length)
plot(dist)

The output is as follows:

Figure 3.36 Plot of the KDE for sepal length

This distribution is closest to the normal distribution, which we studied in the previous section. Here, the mean and median are both around 5.

Calculate and plot the KDE from the kdensity function for sepal width:

dist <- kdensity(df$Sepal.Width)
plot(dist)

The output is as follows:

Figure 3.37 Plot of the KDE for sepal width

Load the Iris dataset into the df variable:

df<-iris

Keep rows with the setosa species only:

df=df[df$Species=='setosa',]

Calculate the mean and standard deviation of the sepal length column of df:

sdev<-sd(df$Sepal.Length)
mn<-mean(df$Sepal.Length)

Generate a new distribution with the standard deviation and mean of the sepal length column:

xnorm<-rnorm(100,mean=mn,sd=sdev)

Plot the CDF of both xnorm and the sepal length column:

plot(ecdf(xnorm),col='blue')
plot(ecdf(df$Sepal.Length),add=TRUE,pch = 4,col='red')

The output is as follows:

Figure 3.38: The CDF of xnorm and sepal length

The samples look very close to each other in the distribution. Let's see, in the next test, whether the sepal length sample belongs to the normal distribution or not.

Perform the Kolmogorov-Smirnov test on the two samples, as follows:

ks.test(xnorm,df$Sepal.Length)

The output is as follows:

    Two-sample Kolmogorov-Smirnov test
data: xnorm and df$Sepal.Length
D = 0.14, p-value = 0.5307
alternative hypothesis: two-sided

Here, p-value is very high and the D value is low, so we can assume that the distribution of sepal length is closely approximated by the normal distribution.

Repeat the same steps for the sepal width column of df:

sdev<-sd(df$Sepal.Width)
mn<-mean(df$Sepal.Width)
xnorm<-rnorm(100,mean=mn,sd=sdev)
plot(ecdf(xnorm),col='blue')
plot(ecdf(df$Sepal.Width),add=TRUE,pch = 4,col='red')

The output is as follows:

Figure 3.39: CDF of xnorm and sepal width

Perform the Kolmogorov-Smirnov test as follows:

ks.test(xnorm,df$Sepal.Length)

The output is as follows:

    Two-sample Kolmogorov-Smirnov test

data: xnorm and df$Sepal.Width
D = 0.12, p-value = 0.7232
alternative hypothesis: two-sided