Gamma distribution in R

Gamma distribution in R, This guide demonstrates how to use R to fit a gamma distribution to a dataset.

Gamma Distribution Fitting in R

Let’s say you have a dataset z that was produced using the following method:

Create 30 random values that are distributed according to a gamma distribution with shape parameters of 4 and 9 along with some gaussian noise.

Gama <- rgamma(30, 4, 9) + rnorm(30, 0, .03)

Now we can view the first 6 values

head(Gama)
[1] 0.1362240 0.5979568 0.4930604 0.2808689 0.4361617

With the help of the fitdistrplus package in R, we can examine how well a gamma distribution fits this dataset Gama.

if not already installed, install the ‘fitdistrplus’ package.

install.packages('fitdistrplus')

Yes, now we can load the package

library(fitdistrplus)

To fit a distribution using this package, the following general syntax should be used:

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

In this instance, we’ll use the gamma distribution and maximum likelihood estimation approach to suit the dataset z that we created earlier:

Using mle, we fitted our dataset to a gamma distribution.

fit <- fitdist(Gama, distr = "gamma", method = "mle")

Let’s view the summary of the fit

summary(fit)

Fitting of the distribution ‘ gamma ‘ by maximum likelihood

Parameters :
      estimate Std. Error
shape 3.551416   0.647940
rate  7.019582   1.375659
Loglikelihood:  -0.1783264   AIC:  4.356653   BIC:  8.371319
Correlation matrix:
          shape      rate
shape 1.0000000 0.9309661
rate  0.9309661 1.0000000

The following syntax can then be used to create several charts that demonstrate how well the gamma distribution fits the dataset.