AcceptReject: An R Package for Acceptance-Rejection Method

The AcceptReject package, available for the R programming language on the Comprehensive R Archive Network (CRAN), versioned and maintained on GitHub, offers a simple and efficient solution for generating pseudo-random observations of discrete or continuous random variables using the acceptance-rejection method. This method provides a viable alternative for generating pseudo-random observations in univariate distributions when the inverse of the cumulative distribution function is not in closed form or when suitable transformations involving random variables that we know how to generate are unknown, thereby facilitating the generation of observations for the variable of interest. The package is designed to be simple, intuitive, and efficient, allowing for the rapid generation of observations and supporting multicore parallelism on Unix-based operating systems. Some components are written using C++, and the package maximizes the acceptance probability of the generated observations, resulting in even more efficient execution. The package also allows users to explore the generated pseudo-random observations by comparing them with the theoretical probability mass function or probability density function and to inspect the underlying probability density functions that can be used in the method for generating observations of continuous random variables. This article explores the package in detail, discussing its functionalities, benefits, and practical applications, and provides various benchmarks in several scenarios.