A flexible wrapped Lindley-type distribution for angular data modelling

TL;DR

This paper introduces the w3PL distribution, a flexible circular model extending the wrapped Lindley distribution with additional shape parameters, enabling better modeling of diverse angular data behaviors.

Contribution

The paper proposes the w3PL distribution, enhancing flexibility in circular data modeling by incorporating extra shape parameters while maintaining analytical tractability.

Findings

Closed-form expressions for density, CDF, and moments derived

Simulation study confirms reliable parameter estimation

Application shows improved fit over existing models

Abstract

Flexible distributions for modelling angular data have received considerable attention in recent years, with ongoing work extending existing circular models to provide greater flexibility in capturing diverse angular behaviours. In this paper, we introduce and study the w3PL distribution, a circular model obtained by extending the wrapped Lindley distribution by incorporating two additional shape parameters. The proposed generalisation increases flexibility in modelling concentration and skewness while preserving analytical tractability and encompassing existing circular models as special cases. Closed-form expressions for the probability density function, cumulative distribution function, and trigonometric moments are derived, allowing key distributional properties to be studied analytically. The distributional modality is characterised, and the nature of invariance is investigated for the newly proposed circular model. Parameter estimation is developed within a regularised maximum likelihood framework, and a simulation study demonstrates reliable parameter recovery and stable finite-sample performance. Applications to angular datasets from geology, marine biology, and finance illustrate the model's practical significance and show improved fit relative to existing circular alternatives.