Gamma Distribution in R Programming – dgamma(), pgamma(), qgamma(), and rgamma() Functions

The Gamma distribution in R Programming Language is defined as a two-parameter family of continuous probability distributions which is used in exponential distribution, Erlang distribution, and chi-squared distribution. This article is about the implementation of functions of the gamma distribution.

dgamma() Function

The dgamma() function is used to create a gamma density plot which is basically used due to exponential and normal distribution factors.

Syntax:

dgamma(x_dgamma, shape) 

Parameters:

• x_dgamma: defines gamma function 
• shape: gamma density of input values 
• Returns: Plot dgamma values

Example :

R

# R program to plot gamma distribution

# Specify x-values for gamma function
x_dgamma <- seq(0, 2, by = 0.04)

# Apply dgamma function
y_dgamma <- dgamma(x_dgamma, shape = 6)

# Plot dgamma values
plot(y_dgamma)

Output :

Gamma Distribution in R

pgamma() Function

The pgamma() function is used in the cumulative distribution function (CDF) of the gamma distribution.

Syntax: pgamma(x_pgamma, shape)

Parameters:

• x_pgamma: defines gamma function 
• shape: gamma density of input values 
• Returns: Plot pgamma values

R

# Specify x-values for gamma function
x_pgamma <- seq(0, 2, by = 0.04)

# Apply pgamma function
y_pgamma <- pgamma(x_pgamma, shape = 6)

# Plot pgamma values
plot(y_pgamma)

Output:

Cumulative Gamma Distribution Function

qgamma() Function

It is known as the gamma quantile function of the gamma distribution and is used to plot qgamma distribution.

Syntax: qgamma(x_qgamma, shape) 

Parameters:

• x_qgamma: defines gamma function 
• shape: gamma density of input values 
• Returns: Plot qgamma values with gamma density

R

# R program to plot gamma distribution

# Specify x-values for gamma function
x_qgamma <- seq(0, 1, by = 0.03)

# Apply qgamma function
y_qgamma <- qgamma(x_qgamma, shape = 6)

# Plot qgamma values
plot(y_qgamma)

Output:

Quantile Function of Gamma Distribution

rgamma() Function

This function is basically used for generating random numbers in gamma distribution.

Syntax:

rgamma(N, shape)

Parameters:

• N: gamma distributed values 
• shape: gamma density of input values 
• Returns: Plot rgamma values with gamma density

R

# R program to plot gamma distribution

# Set seed for reproducibility
set.seed(1200)

# Specify sample size
N <- 800

# Draw N gamma distributed values
y_rgamma <- rgamma(N, shape = 5)

# Print values to RStudio console
y_rgamma

# Plot of randomly drawn gamma density
hist(y_rgamma, breaks = 500,
     main = "")

Output:

Histogram of 100 Gamma Distributed Numbers