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)

**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