The wrapped XLindley distribution

Abstract In the study of many environmental phenomena, circular statistical analysis and applications to directional data are crucial. In this paper, we introduce the wrapped XLindley distribution, a novel circular distribution with a single parameter. We derive expressions for the distribution’s characteristic function, trigonometric moments, and other associated descriptive measures. The unknown distributional parameter is estimated using the maximum likelihood, least squares, and weighted least squares approach, and the accuracy of these estimates is tested using a simulation study. Finally, to clarify the suggested distribution’s modeling potential, we fit the proposed model to two circular real-world data sets and evaluate the goodness of fit of this distribution in comparison to the wrapped Lindley, wrapped modified Lindley, Von Mises, Jones–Pewsey, and Kato–Jones distributions.