# Exponential Distribution in R (4 Examples) | dexp, pexp, qexp & rexp Functions

This tutorial explains how to **apply the exponential functions** in the R programming language.

The content of the article looks as follows:

- Example 1: Exponential Density in R (dexp Function)
- Example 2: Exponential Cumulative Distribution Function (pexp Function)
- Example 3: Exponential Quantile Function (qexp Function)
- Example 4: Random Number Generation (rexp Function)
- Video & Further Resources

Let’s get started…

## Example 1: Exponential Density in R (dexp Function)

Let’s begin with the exponential density.

We can use the dexp R function return the corresponding values of the exponential density for an input vector of quantiles.

Let’s create such a vector of quantiles in RStudio:

x_dexp <- seq(0, 1, by = 0.02) # Specify x-values for exp function |

x_dexp <- seq(0, 1, by = 0.02) # Specify x-values for exp function

Now, we can apply the dexp function with a rate of 5 as follows:

y_dexp <- dexp(x_dexp, rate = 5) # Apply exp function |

y_dexp <- dexp(x_dexp, rate = 5) # Apply exp function

We can use the plot function to create a graphic, which is showing the exponential density based on the previously specified input vector of quantiles:

plot(y_dexp) # Plot dexp values |

plot(y_dexp) # Plot dexp values

**Figure 1: Exponential Density in R.**

## Example 2: Exponential Cumulative Distribution Function (pexp Function)

We can also use the R programming language to return the corresponding values of the exponential cumulative distribution function for an input vector of quantiles. Again, let’s create such an input vector:

x_pexp <- seq(0, 1, by = 0.02) # Specify x-values for pexp function |

x_pexp <- seq(0, 1, by = 0.02) # Specify x-values for pexp function

In order to get the values of the exponential cumulative distribution function, we need to use the pexp function:

y_pexp <- pexp(x_pexp, rate = 5) # Apply pexp function |

y_pexp <- pexp(x_pexp, rate = 5) # Apply pexp function

We can draw a plot of our previously extracted values as follows:

plot(y_pexp) # Plot pexp values |

plot(y_pexp) # Plot pexp values

**Figure 2: Exponential Cumulative Distribution Function.**

## Example 3: Exponential Quantile Function (qexp Function)

Similar to Examples 1 and 2, we can use the qexp function to return the corresponding values of the quantile function. This time, we need to specify a vector oft probabilities:

x_qexp <- seq(0, 1, by = 0.02) # Specify x-values for qexp function |

x_qexp <- seq(0, 1, by = 0.02) # Specify x-values for qexp function

The qexp command can then be used to get the quantile function values…

y_qexp <- qexp(x_qexp, rate = 5) # Apply qexp function |

y_qexp <- qexp(x_qexp, rate = 5) # Apply qexp function

…and we can also draw a scatterplot containing these values:

plot(y_qexp) # Plot qexp values |

plot(y_qexp) # Plot qexp values

**Figure 3: Exponential Quantile Function.**

## Example 4: Random Number Generation (rexp Function)

In R, we can also draw random values from the exponential distribution.

First, we need to specify a seed and the sample size we want to simulate:

set.seed(13579) # Set seed for reproducibility N <- 10000 # Specify sample size |

set.seed(13579) # Set seed for reproducibility N <- 10000 # Specify sample size

Then, we can use the rexp function as follows:

y_rexp <- rexp(N, rate = 5) # Draw N exp distributed values y_rexp # Print values to RStudio console |

y_rexp <- rexp(N, rate = 5) # Draw N exp distributed values y_rexp # Print values to RStudio console

We can create a histogram of our randomly sampled values as follows:

hist(y_rexp, breaks = 100, main = "") # Plot of randomly drawn exp density |

hist(y_rexp, breaks = 100, main = "") # Plot of randomly drawn exp density

**Figure 4: Histogram of Random Numbers Drawn from Exponential Distribution.**

## Video & Further Resources

If you need further info on the examples of this article, you may want to have a look at the following video of the Statistics Globe YouTube channel. I’m explaining the R programming code of this tutorial in the video.

*The YouTube video will be added soon.*

You might also read the other tutorials on probability distributions and the generation of random numbers in R:

- Bernoulli Distribution in R
- Beta Distribution in R
- Binomial Distribution in R
- Bivariate & Multivariate Distributions in R
- Cauchy Distribution in R
- Chi-Squred Distribution in R
- Exponential Distribution in R
- F Distribution in R
- Gamma Distribution in R
- Geometric Distribution in R
- Hypergeometric Distribution in R
- Log Normal Distribution in R
- Logistic Distribution in R
- Negative Binomial Distribution in R
- Normal Distribution in R
- Poisson Distribution in R
- Student t Distribution in R
- Studentized Range Distribution in R
- Uniform Distribution in R
- Weibull Distribution in R
- Wilcoxon Signedank Statistic Distribution in R
- Wilcoxonank Sum Statistic Distribution in R

In addition, you may read some of the other articles of my homepage:

In this post, I explained how to **use the exponential functions and how to simulate random numbers with exponential growth** in R. In case you have any further comments or questions, please let me know in the comments.

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