How to Use the Gamma Distribution in R (With Examples)

In statistics, the gamma distribution is often used to model probabilities related to waiting times.

We can use the following functions to work with the gamma distribution in R:

dgamma(x, shape, rate) – finds the value of the density function of a gamma distribution with certain shape and rate parameters.
pgamma(q, shape, rate) – finds the value of the cumulative density function of a gamma distribution with certain shape and rate parameters.
qgamma(p, shape, rate) – finds the value of the inverse cumulative density function of a gamma distribution with certain shape and rate parameters.
rgamma(n, shape, rate) – generates n random variables that follow a gamma distribution with certain shape and rate parameters.

The following examples show how to use each of these functions in practice.

Example 1: How to Use dgamma()

The following code shows how to use the dgamma() function to create a probability density plot of a gamma distribution with certain parameters:

#define x-values
x <- seq(0, 2, by=0.01)   
  
#calculate gamma density for each x-value
y <- dgamma(x, shape=5) 
  
#create density plot
plot(y)

Example 2: How to Use pgamma()

The following code shows how to use the pgamma() function to create a cumulative density plot of a gamma distribution with certain parameters:

#define x-values
x <- seq(0, 2, by=0.01)   
  
#calculate gamma density for each x-value
y <- pgamma(x, shape=5) 
  
#create cumulative density plot
plot(y)

Example 3: How to Use qgamma()

The following code shows how to use the qgamma() function to create a quantile plot of a gamma distribution with certain parameters:

#define x-values
x <- seq(0, 1, by=0.01)   
  
#calculate gamma density for each x-value
y <- qgamma(x, shape=5) 
  
#create quantile plot
plot(y)

Example 4: How to Use rgamma()

The following code shows how to use the rgamma() function to generate and visualize 1,000 random variables that follow a gamma distribution with a shape parameter of 5 and a rate parameter of 3:

#make this example reproducible
set.seed(0)

#generate 1,000 random values that follow gamma distribution
x <- rgamma(n=1000, shape=5, rate=3)

#create histogram to view distribution of values
hist(x)