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

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.

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 = "")

Output:

Histogram of 100 Exponentially Distributed Numbers