Wrapped New One-Parameter Distribution: Properties, Simulation and Application using Wind Direction Dataset

Abstract

Circular data arise in many scientific disciplines where observations are directions, angles, or time-of-day values measured on a circle. Classical statistical techniques are inadequate in such contexts due to the periodic nature of the data. Wrapped distributions offer a natural way to model such data by projecting linear distributions onto the unit circle. In this paper, we introduce a new wrapped distribution derived from a Rayleigh-type base distribution, called the Wrapped New One-Parameter Distribution (WNOPD). The WNOPD is a one-parameter, unimodal, asymmetric distribution that can model a wide range of circular data. We derive its key statistical properties, including the trigonometric moments, characteristic function, and circular skewness and kurtosis. Maximum likelihood estimation is useto estimate the model parameters, and its performance is evaluated via simulation studies. A real data application to wind direction data demonstrates the superior fit of the WNOPD compared to existing wrapped and classical circular distributions. The model's simplicity, interpretability, and strong empirical performance suggest it is a useful tool for directional data analysis.