How to Fit a Gamma Distribution to a Dataset in R

The Gamma distribution is specifically used to determine the exponential distribution, Erlang distribution, and chi-squared distribution. It is also referred to as the two-parameter family having the continuous probability distribution.

Stepwise Implementation

Step 1: Install and import the fitdistrplus package in the R:

install.package("fitdistrplus")
library(fitdistrplus)

The fitdistrplus package provides us fitdist function to fit a distribution.

Syntax:

fitdist(dataset, distr = “choice”, method = “method”)

Here,

• distr = “choice” : It represents the distribution choice
• method = “method” : It represents the method of fitting the data

Step 2: Now, we would fit the dataset data with the help of the gamma distribution and with the help of the maximum likelihood estimation approach to fit the dataset.

R

# Generating 20 random values that uses
# a gamma distribution having shape
# parameter as 10
# combined with some gaussian noise
data <- rgamma(20, 3, 10) + rnorm(20, 0, .02)

# Fit the dataset to a gamma distribution
# using mle
ans <- fitdist(data, distr = "gamma", method = "mle")

# Display the summary of ans
summary(ans)

Output:

Now we will produce some plots that will show how well the gamma distribution fits the dataset with the help of the below syntax.

R

# Import the package
library(fitdistrplus)

# Generating 20 random values that uses a
# gamma distribution having shape parameter
# as 10
# combined with some gaussian noise
data <- rgamma(20, 3, 10) + rnorm(20, 0, .02)

# Fitting the dataset to a gamma distribution
# with the help of mle
ans <- fitdist(data, distr = "gamma", method = "mle")

# Display the plot
plot(ans)

Output:

Example:

R

# Import the package
library(fitdistrplus)

# Generating 20 random values that uses a
# gamma distribution having shape parameter
# as 10
# combined with some gaussian noise
data <- rgamma(20, 3, 10) + rnorm(20, 0, .02)

# Fitting the dataset to a gamma distribution
# with the help of mle
ans <- fitdist(data, distr = "gamma", method = "mle")

# Display the summary of the ans
summary(ans)

# Display the plot
plot(ans)

Output: