Plot Probability Distribution Function in R

The PDF is the acronym for Probability Distribution Function and CDF is the acronym for Cumulative Distribution Function. In general, there are many probability distribution functions in R in this article we are going to focus on the Normal Distribution among them to plot PDF. 

To calculate the Normal Distribution Function we have the built-in function dnorm() and to calculate the CDF we have ecdf() in R programming Language.

Syntax:

PDF: dnorm(x,mean,sd)

CDF: ecdf(x)

where, 

• x – the data vector
• mean – mean of the data to calculated or can be assigned to a value
• sd – standard deviation of the data to be calculated or can be assigned to a value

Using plot() function to plot PDF

In this, we will use dnom() function to calculate the normal distribution based on the mean and standard deviation of the data.

R

# Generating sequence of
# numbers from -15 to +10
x<-seq(-15,10)

# calculate the Normal distribution function
# based on the mean and sd of data
pdf<- dnorm(x,mean(x),sd(x))

# Plotting the PDF(Normal Distribution Function
plot(x,pdf)

Output:

Using plotpdf() function to plot PDF

The plotpdf() is a function which is present in gbutils package. 

# install gbutils package
install.packages("gbutils")

This package is specifically developed to simulate Quantile plots in R Programming. plotpdf() function used to plot PDF on Y-axis and  the quantiles of the distribution on X- axis.

Syntax: plotpdf(pdf, qdf, lq, uq)

Where,

• pdf – Probability Distribution Function to be plotted is specified here
• qdf – The quantile function to be used is specified here
• lq  – lower quantile need to be used in computation
• uq  – upper quantile need to be used in computation

R

# Load the installed package
library(gbutils)

# Generating sequence of numbers from -50 to +10
x<-seq(-50,10)

# Calculate the Normal distribution
# function based on the mean and sd of data
pdf<- dnorm(x,mean(x),sd(x))

# Calculate the Quantile distribution
# function based on the mean and sd of data
qdf <- function(x) qnorm(x, mean(x), sd(x))

# Plotting the PDF Normal Distribution Function
gbutils::plotpdf(pdf,qdf,lq=0.0001,uq=0.0009)

Output:

Using plot() function to plot CDF

In this, we will use ecdf() function to calculate the cumulative distribution based on the mean and standard deviation of the data. 

R

# Generating sequence of
# numbers from -15 to +10
x<-seq(-15,10)

# calculate the Cumulative distribution
# function based on the mean and sd of data
cdf<-ecdf(x)

# Plotting the CDF
plot(cdf,xlabel="x",ylabel="y",main="CDF Graph")

Output:

Using plotpdf() function to plot the CDF

The plotpdf() is a function which is present in gbutils package. This package is specifically developed to simulate Quantile plots in R Programming. plotpdf() function used to plot CDF.

Syntax: plotpdf(pdf, qdf, lq, uq)

Where,

•   cdf – Cumulative Density to be plotted is specified here
• qdf –  The quantile function to be used is specified here
• lq – lower quantile need to be used in computation
• uq – upper quantile need to be used in computation

R

# install and load the gbutils package
install.packages("gbutils")
library(gbutils)

# Calculating the CDF Normal Distribution Function
cdf1 <- function(x)pnorm(x, mean = -2.5, sd = 7.64)

# Plotting the CDF Normal Distribution Function
gbutils::plotpdf(cdf1, cdf = cdf1,main='CDF Plot')

Output: