A New Wrapped Discrete Linear Exponential Distribution for Circular Data: Theory, Estimation, and Applications

The analysis of circular data with discrete models has been a challenge. To address this, we introduce the wrapped discrete linear exponential (WDLE) distribution, which is a new model obtained by wrapping the existing discrete linear exponential distribution around the unit circle. Notably, the probability mass function of the WDLE model can be stated as a mixture of a wrapped geometric distribution and a wrapped discrete gamma distribution, making it a simpler and more understandable model for dealing with circular data. This model includes closed-form formulas for essential distributional properties such as the characteristic function, trigonometric moments, and circular measures of location and dispersion, making it suitable for use in a variety of practical applications. Maximum likelihood is used for parameter estimation, and simulation studies are used to assess performance. The effectiveness of the model for circular data analysis was confirmed by applying it to two real-world datasets, where it demonstrated higher performance under various information criteria.