Wrapped: An R package for circular data

Area of Science:

• Statistics
• Computational Statistics

Background:

• Wrapped distributions are essential for modeling circular data in various fields.
• Existing statistical software may lack comprehensive support for a wide range of univariate wrapped distributions.

Purpose of the Study:

• To introduce the 'Wrapped' R package, a novel tool for analyzing univariate wrapped distributions.
• To provide a unified and efficient computational framework for probability, quantile, and sampling functions.
• To implement robust statistical estimation and model-fitting capabilities for these distributions.

Main Methods:

• The package implements core statistical functions: probability density function (PDF), cumulative distribution function (CDF), and quantile function.
• It includes functions for generating random variates from various univariate wrapped distributions.
• Maximum likelihood estimation (MLE), standard error calculation, confidence interval determination, and goodness-of-fit measures are incorporated.

Main Results:

• The 'Wrapped' package successfully computes PDF, CDF, and quantiles for numerous univariate wrapped distributions.
• It enables the generation of random samples, facilitating simulations and further analysis.
• The package provides reliable estimation of parameters, standard errors, confidence intervals, and goodness-of-fit statistics for approximately fifty distributions.

Conclusions:

• The 'Wrapped' R package offers a valuable and comprehensive resource for statisticians and data scientists working with circular data.
• Its extensive functionality and robust estimation methods enhance the analysis of univariate wrapped distributions.
• The package is supported by numerical illustrations, demonstrating its practical utility.