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R is a widely used statistical programming language that offers powerful tools for data analysis and modeling. One of these tools is the ability to fit a Gamma distribution to a given dataset. The Gamma distribution is a commonly used statistical distribution that is often used to model continuous, positively skewed data. To fit a Gamma distribution to a dataset in R, one can use the “fitdistr” function from the “MASS” package. This function allows for the estimation of the parameters of the Gamma distribution based on the given dataset, as well as providing useful summary statistics and visualizations of the fitted distribution. By utilizing R’s capabilities, one can accurately model and analyze data that follows a Gamma distribution, allowing for better understanding and interpretation of the data.
Fit a Gamma Distribution to a Dataset in R
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)