The Extended Laplace Distribution

Provides computational tools for working with the Extended Laplace distribution, including the probability density function, cumulative distribution function, quantile function, random variate generation based on convolution with Uniform noise and the quantile-quantile plot. Useful for modeling contaminated Laplace data and other applications in robust statistics. See Saah and Kozubowski (2025) .

ExtendedLaplace

ExtendedLaplace: Extended Laplace Distribution

The ExtendedLaplace R package provides functions for the probability density function (dEL()), cumulative distribution function (pEL()), quantile function (qEL()), random number generation (rEL()) and QQ-plot for the Extended Laplace distribution, developed to model contaminated Laplace data with additional uniform errors.

This distribution generalizes the classical Laplace distribution by convolving it with a uniform distribution, which allows for modeling error-prone data in a more robust way.

Developed by:

Saah, D. K., & Kozubowski, T. J. (2025).
A new class of extended Laplace distributions with applications to modeling contaminated Laplace data.
Journal of Computational and Applied Mathematics.
https://doi.org/10.1016/j.cam.2025.116588

Installation

You can install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("saahdavid/ExtendedLaplace")

Once submitted to CRAN, you can install it using:

install.packages("ExtendedLaplace")

Functions

• dEL(y, mu, sigma, delta): Density function
• pEL(y, mu, sigma, delta): Cumulative distribution function
• qEL(u, mu, sigma, delta): Quantile function
• rEL(n, mu, sigma, delta): Random number generation
• qqplotEL(samples, mu, sigma, delta): Quantile-Quantile Plot

Example

library(ExtendedLaplace)

# PDF at y = 0
mu <- 0; sigma <- 1; delta <- 1
dEL(0, mu, sigma, delta)

# CDF at y = 0
pEL(0, mu, sigma, delta)

# Quantile at 0.5 (median)
qEL(0.5, mu, sigma, delta)

# Generate 1000 samples
set.seed(123)
samples <- rEL(1000, mu, sigma, delta)
hist(samples, breaks = 50, freq = FALSE)
curve(dEL(x, mu, sigma, delta), add = TRUE, col = "blue", lwd = 2)

# QQ-Plot 
qqplotEL(samples, mu, sigma, delta)

Authors

David K. Saah ORCID: 0009-0006-8049-3627 Email: [email protected]

Tomasz J. Kozubowski Email: [email protected]

License

MIT License (see LICENSE file)