The Extended Laplace Distribution.

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)