Modeling and Applications to Circular Data with a Wrapped Poisson-Lindley Model (Journal of Mathematical Study, 2022)
In the recent years, researchers in many fields, including meteorology, economics, sociology, psychology, and epidemiology, have shown a keen interest in the analysis and modeling of wrapped data. This motivates the development of new wrapped distributions and related models. In this paper, a simple and new wrapped model based on the Poisson-Lindley distribution is developed. Many of its properties are obtained, such as probability mass and cumulative distribution functions, survival and hazard rate functions, and probability generating function. The estimation of the model parameter is investigated by the maximum likelihood method. Test and evaluation statistics are also considered to assess the performance of the distribution among the most frequently wrapped discrete probability models using  three different circular practical data sets.