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 #calculate gamma density for each x-value
y #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 #calculate gamma density for each x-value
y #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 #calculate gamma density for each x-value
y #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 #create histogram to view distribution of values
hist(x)

Additional Resources

The following tutorials explain how to use other common statistical distributions in R:

How to Use the Normal Distribution in R
How to Use the Binomial Distribution in R
How to Use the Poisson Distribution in R
How to Use the Geometric Distribution in R