# Negative Binomial Distribution in R (4 Examples) | dnbinom, pnbinom, qnbinom & rnbinom Functions

This article illustrates how to use the negative binomial functions in the R programming language.

The content of the article looks as follows:

Sound good? Here’s how to do it…

## Example 1: Negative Binomial Density in R (dnbinom Function)

Example 1 explains how to create an R graphic showing the negative binomial density. As a first step, we need to create a sequence with non-negative integers in R:

`x_dnbinom <- seq(0, 100, by = 1) # Specify x-values for dnbinom function`

Now, we can use the dnbinom R function to return the corresponding negative binomial values of each element of our input vector with non-negative integers. Note that we are using a size (i.e. number of trials) and a probability of 0.5 (i.e. 50%) in this example:

`y_dnbinom <- dnbinom(x_dnbinom, size = 100, prob = 0.5) # Apply dnbinom function`

Based on the plot function of the R programming language, we can create a graph showing our output:

`plot(y_dnbinom) # Plot dnbinom values` Figure 1: Negative Binomial Density in R.

## Example 2: Negative Binomial Cumulative Distribution Function (pnbinom Function)

In the second example, I’ll show you how to plot the cumulative distribution function of the negative binomial distribution based on the pnbinom command.

Again, we need to create a sequence on non-negative integers as input for the pnbinom function:

`x_pnbinom <- seq(0, 100, by = 1) # Specify x-values for pnbinom function`

The pnbinom function is now applied as follows…

`y_pnbinom <- pnbinom(x_pnbinom, size = 100, prob = 0.5) # Apply pnbinom function`

…and we can create a plot illustrating the output of pnbinom as follows:

`plot(y_pnbinom) # Plot pnbinom values` Figure 2: Negative Binomial Cumulative Distribution Function.

## Example 3: Negative Binomial Quantile Function (qnbinom Function)

Similar to the R syntax of Examples 1 and 2, we can create a plot containing the negative binomial quantile function. As input, we need to specify a vector of probabilities:

`x_qnbinom <- seq(0, 1, by = 0.01) # Specify x-values for qnbinom function`

We can now apply the qnbinom function to these probabilities as shown in the R code below:

`y_qnbinom <- qnbinom(x_qnbinom, size = 100, prob = 0.5) # Apply qnbinom function`

A plot of the output of qnbinom can be created as follows:

`plot(y_qnbinom) # Plot qnbinom values` Figure 3: Negative Binomial Quantile Function.

## Example 4: Simulation of Random Numbers (rnbinom Function)

In order to generate a set of random numbers that are following the negative binomial distribution, we need to specify a seed and a sample size first:

```set.seed(53535) # Set seed for reproducibility N <- 10000 # Specify sample size```

We can now draw a set of random numbers of this sample size as follows:

```y_rnbinom <- rnbinom(N, size = 100, prob = 0.5) # Draw N nbinomially distributed values y_rnbinom # Print values to RStudio console # 102 102 89 96 94 74 92 112 87 99 87 131 109...```

The following histogram illustrates the RStudio output of our previous R code:

```hist(y_rnbinom, # Plot of randomly drawn nbinom density breaks = 100, main = "")``` Figure 4: Simulation of Random Numbers Based on Negative Binomial Distribution.

## Video, Further Resources & Summary

Have a look at the following video of my YouTube channel. In the video, I explain the R code of this article:

You may also have a look at the other articles on probability distributions and the simulation of random numbers in the R programming language:

Besides that, you could have a look at the other tutorials on my homepage. A selection of posts can be found here.

This article showed how to create and simulate a negative binomial distribution in the R programming language. Don’t hesitate to let me know in the comments section below, if you have additional questions.

Subscribe to the Statistics Globe Newsletter