On wrapping a new version of Lindley distribution for circular data analysis

The wrapped approach is one of the most widely used methods for constructing circular distributions. In this work, we introduce a novel circular distribution generated from wrapping a new XLindley density on the real line around a circle. We have found formulas for the probability density function, the cumulative density function, the characteristic function, the trigonometric moments, and other related descriptive measures of our new model. Our model’s parameters have been estimated using sixteen different estimation techniques. Additionally, the performance of the recommended estimation methods is investigated and assessed through numerical simulation. To clarify the recommended model’s modeling capability, the model is finally fitted to two real-life circular data sets, and its performance is contrasted with that of other models.