This tutorial explains how to fit a gamma distribution to a dataset in R.

Fitting a Gamma Distribution in R

Suppose you have a dataset z that was generated using the approach below:

#generate 50 random values that follow a gamma distribution with shape parameter = 3
#and shape parameter = 10 combined with some gaussian noise
z <- rgamma(50, 3, 10) + rnorm(50, 0, .02)

#view first 6 values
head(z)
[1] 0.07730 0.02495 0.12788 0.15011 0.08839 0.09941

To see how well a gamma distribution fits this dataset z, we can use the fitdistrplus package in R:

#install 'fitdistrplus' package if not already installed
install.packages('fitdistrplus')

#load package
library(fitdistrplus)

The general syntax to use to fit a distribution using this package is:

fitdist(dataset, distr = “your distribution choice”, method = “your method of fitting the data”)

In this case, we will fit the dataset z that we generated earlier using the gamma distribution and maximum likelihood estimation approach to fitting the data:

#fit our dataset to a gamma distribution using mle
fit <- fitdist(z, distr = "gamma", method = "mle")

#view the summary of the fit 
summary(fit)

This produces the following output:

Next, we can produce some plots that show how well the gamma distribution fits the dataset using the following syntax:

#produce plots
plot(fit)

This produces the following plots:

Here is the complete code we used to fit a gamma distribution to a dataset in R:

#install 'fitdistrplus' package if not already installed
install.packages('fitdistrplus')

#load package
library(fitdistrplus)

#generate 50 random values that follow a gamma distribution with shape parameter = 3
#and shape parameter = 10 combined with some gaussian noise
z <- rgamma(50, 3, 10) + rnorm(50, 0, .02)

#fit our dataset to a gamma distribution using mle
fit <- fitdist(z, distr = "gamma", method = "mle")

#view the summary of the fit
summary(fit)

#produce plots to visualize the fit
plot(fit)