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, there are 4 built-in functions to generate exponential distribution:

• dexp()

  dexp(x_dexp, rate) 

• pexp()

  pexp(x_pexp, rate )

• qexp()

  qexp(x_qexp, rate)

• rexp()

  rexp(N, rate )

where,

x: represents x-values for exp function .
rate: represents the shapex.
N: Specify sample size

Functions To Generate Exponential Distribution

dexp() Function

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

Syntax:

dexp(x_dexp, rate)

Example:

# 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:

pexp() Function

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

Syntax:

pexp(x_pexp, rate )

Example:

# 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 :

qexp() Function

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)

Example:

# 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:

rexp() Function

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

Syntax:

rexp(N, rate )

Example:

# 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 :