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

The Gamma distribution in R 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 the implementation of functions of gamma distribution.

dgamma() Function

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

Syntax:
dgamma(x_dgamma, shape)

Parameters:
x_dgamma: defines gamma function
shape: gamma density of input values

Returns: Plot dgamma values

Example :

# 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 :

pgamma() Function

pgamma() function is used in 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

Example:

# R program to plot gamma distribution

# 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:

qgamma() Function

It is known as gamma quantile function of the gamma distribution and 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

Example :

# 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:

rgamma() Function

This function is basically used for generating random number 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

Example :

# 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: