Bernoulli Distribution in R (4 Examples) | dbern, pbern, qbern & rbern Functions


In this R tutorial you’ll learn how to apply the Bernoulli distribution functions.

Table of contents:

Let’s start right away.


Example 1: Bernoulli Probability Density Function (dbern Function)

In the first example, I’ll show you how to draw a plot of the probability density function (PDF) of the Bernoulli distribution.

The base installation of R does not provide any Bernoulli distribution functions. For that reason, we need to install and load the Rlab add-on package first:

install.packages("Rlab")                         # Install Rlab package
library("Rlab")                                  # Load Rlab package

Then, we need to create a vector of quantiles in R:

x_dbern <- seq(0, 10, by = 1)                    # Specify x-values for dbern function

We can now apply the dbern function of the Rlab R package to our vector of quantiles in order to return the corresponding values of the Bernoulli PDF:

y_dbern <- dbern(x_dbern, prob = 0.7)            # Apply dbern function

If we want to draw a graphic of this distribution, we can apply the plot function as shown below:

plot(y_dbern, type = "o")                        # Plot dbern values


Bernoulli probability density function plot in R

Figure 1: PDF of Bernoulli Distribution in R.


Example 2: Bernoulli Cumulative Distribution Function (pbern Function)

The R syntax for the cumulative distribution function of the Bernoulli distribution is similar as in Example 1. First, we have to create a vector of quantiles:

x_pbern <- seq(0, 10, by = 1)                    # Specify x-values for pbern function

Then, we can apply the pbern function to this vector:

y_pbern <- pbern(x_pbern, prob = 0.7)            # Apply pbern function

And finally, we can create a graph of the output of pbern with the plot function:

plot(y_pbern, type = "o")                        # Plot pbern values


Bernoulli cumulative distribution function plot in R

Figure 2: CDF of Bernoulli Distribution in R.


Example 3: Bernoulli Quantile Function (qbern Function)

Example 3 shows how to create a graphic of the quantile function of the Bernoulli distribution. As a first step, we have to create a sequence of probabilities (i.e. values between 0 and 1):

x_qbern <- seq(0, 1, by = 0.1)                   # Specify x-values for qbern function

We can now use the qbern function to get the corresponding quantile function values for our probabilities:

y_qbern <- qbern(x_qbern, prob = 0.7)            # Apply qbern function

The corresponding plot can be drawn with the plot function:

plot(y_qbern, type = "o")                        # Plot qbern values


Bernoulli quantile function plot in R

Figure 3: Quantile Function of Bernoulli Distribution in R.


Example 4: Generating Random Numbers (rbern Function)

To generate a set of random numbers with a Bernoulli distribution, we need to specify a seed and a sample size N first:

set.seed(98989)                                  # Set seed for reproducibility
N <- 10000                                       # Specify sample size

Then, we can apply the rbern function to create N Bernoulli distributed random numbers:

y_rbern <- rbern(N, prob = 0.7)                  # Draw N random values
y_rbern                                          # Print values to RStudio console

We can illustrate the output of the rbern function with a histogram:

hist(y_rbern,                                    # Plot of randomly drawn density
     breaks = 5,
     main = "")


Bernoulli random numbers plot in R

Figure 4: Randomly Drawn Numbers of Bernoulli Distribution in R.


Video, Further Resources & Summary

If you need further info on the R codes of this tutorial, you may watch the following video of my YouTube channel. I illustrate the R syntax of this page in the video:


The YouTube video will be added soon.


You may also have a look at the other tutorials on distributions and the simulation of random numbers in R:


In addition, I can recommend to have a look at some of the related tutorials of my homepage.


This article showed how to use the dbern, pbern, qbern, and rbern functions of the Rlab package in the R programming language. Let me know in the comments below, if you have additional questions. Furthermore, don’t forget to subscribe to my email newsletter for regular updates on the newest articles.


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