Overview

The skellam package provides functions for working with the Skellam distribution – the distribution of the difference between two independent Poisson random variables. It includes routines for:

• Calculating the probability mass function (dskellam)
• Computing the cumulative distribution function (pskellam)
• Determining quantiles (qskellam)
• Generating random variates (rskellam)
• Performing maximum likelihood estimation (skellam.mle)
• Conducting regression analysis under the Skellam model (skellam.reg)

This package is designed to offer enhanced numerical accuracy and robust handling of a wide range of parameter values.

Installation

Install the latest stable version from CRAN:

install.packages("skellam")

Alternatively, install the development version from GitHub:

# install.packages("remotes")  # Uncomment if needed
remotes::install_github("monty-se/skellam")

Usage

Distribution Functions

dskellam(x, lambda1, lambda2 = lambda1, log = FALSE)

Returns the (log) density of the Skellam distribution.

pskellam(q, lambda1, lambda2 = lambda1, lower.tail = TRUE, log.p = FALSE)

Computes the (log) cumulative distribution function.

qskellam(p, lambda1, lambda2 = lambda1, lower.tail = TRUE, log.p = FALSE)

Returns the quantile function for the Skellam distribution.

rskellam(n, lambda1, lambda2 = lambda1)

Generates random variates following the Skellam distribution.

Additional Functionalities

skellam.mle(x)

Performs maximum likelihood estimation (MLE) for the Skellam distribution parameters based on observed differences.

skellam.reg(y, x)

Fits a regression model assuming a Skellam distribution, using an exponential link to ensure positivity of the rate parameters.

Theoretical Background

If