# 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:

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