Good distribution modelling with the R package good

TL;DR

This paper introduces the R package 'good' for flexible modeling of count data exhibiting over-dispersion or under-dispersion, filling a gap in available statistical tools.

Contribution

The paper presents the first R package for the Good distribution, enabling probabilistic calculations, sampling, and regression modeling for under- and over-dispersed count data.

Findings

Successfully applied to real-world data with over- and under-dispersion

Provides functions for probability, quantiles, and sampling from the Good distribution

Includes a regression framework similar to glm for count data

Abstract

Although models for count data with over-dispersion have been widely considered in the literature, models for under-dispersion -- the opposite phenomenon -- have received less attention as it is only relatively common in particular research fields such as biodosimetry and ecology. The Good distribution is a flexible alternative for modelling count data showing either over-dispersion or under-dispersion, although no R packages are still available to the best of our knowledge. We aim to present in the following the R package good that computes the standard probabilistic functions (i.e., probability density function, cumulative distribution function, and quantile function) and generates random samples from a population following a Good distribution. The package also considers a function for Good regression, including covariates in a similar way to that of the standard glm function. We finally show the use of such a package with some real-world data examples addressing both over-dispersion and especially under-dispersion.