Exponential Distribution in R Programming – dexp(), pexp(), qexp(), and rexp() Functions

Last Updated : 11 Mar, 2024

The exponential distribution in R Language is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. In R Programming Language, there are 4 built-in functions to generate exponential distribution:

Function	Description
dexp	Probability Density Function
pexp	Cumulative Distribution Function
qexp	Quantile Function of Exponential Distribution
rexp	Generating random numbers which are Exponentially Distributed

What is Exponential Distribution?

A random variable X is said to be exponentially distributed if it has a mean equal to 1 / λ and variance is equal to 1 / λ² then that variable is known as Exponential Distribution.

[Tex]f\left(x \right ) = \lambda\; e^{-\lambda x}[/Tex]

dexp() Function

The dexp() function returns the corresponding values of the exponential density for an input vector of quantiles.

Syntax: dexp(x_dexp, rate)

Example:

R

# R program to illustrate
# exponential distribution
# Specify x-values
x_dexp <- seq(1, 10, by = 0.1) 
      
# Apply dexp() function               
y_dexp <- dexp(x_dexp, rate = 5)    
                
# Plot dexp values 
plot(y_dexp)

Output:

Exponential Distribution in R

pexp() Function

The pexp() function returns the corresponding values of the exponential cumulative distribution function for an input vector of quantiles.

Syntax: pexp(x_pexp, rate )

R

# R program to illustrate
# exponential distribution
 
# Specify x-values
x_pexp <- seq(1, 10, by = 0.2)                                     
 
# Apply pexp() function
y_pexp <- pexp(x_pexp, rate = 1) 
 
# Plot values                  
plot(y_pexp)                                                    

Output :

Cumulative Exponential Distribution Function

qexp() Function

The qexp() function gives the possibility, we can use the qexp function to return the corresponding values of the quantile function.

Syntax: qexp(x_qexp, rate)

R

# R program to illustrate
# exponential distribution
 
# Specify x-values 
x_qexp <- seq(0, 1, by = 0.2)                     
  
# Apply qexp() function
y_qexp <- qexp(x_qexp, rate = 1)
  
# Plot values                   
plot(y_qexp)                                       

Output:

Quantile Function of Exponential Distribution

rexp() Function

The rexp() function is used to simulate a set of random numbers drawn from the exponential distribution.

Syntax: rexp(N, rate )

R

# R program to illustrate
# exponential distribution
 
# Set seed for reproducibility
set.seed(500) 
 
# Specify size         
N <- 100
 
# Draw exp distributed values
y_rexp <- rexp(N, rate = 1)
  
# Plot exp density  
hist(y_rexp, breaks = 50, main = "")