The Wrapped Q-Lindley Distribution: A New Circular Model with Statistical Properties, Classical and Bayesian Inference, and Applications to Directional Data
- 1Department of Statistics, Dibrugarh University, Dibrugarh 786004, Assam, India
- 2Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
- 3Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Abstract
Circular data arise naturally in a wide range of scientific fields, including biology, geology, meteorology, and environmental sciences, where conventional linear statistical methods are inappropriate unless the circular structure of the observations is taken into account. Motivated by the need for parsimonious, analytically tractable models for unimodal directional data, we introduce a new one-parameter circular model, the Wrapped Q-Lindley (WQL) distribution. The proposed model is obtained by wrapping the Q-Lindley distribution and has a specific unimodal asymmetric shape. Closed-form or analytically tractable expressions are derived for several important distributional properties, including the characteristic function, trigonometric moments, circular descriptive measures, and Rényi entropy. We investigate parameter estimation using ten classical estimation methods, along with Bayesian inference, under four symmetric and asymmetric loss functions. A Monte Carlo simulation study evaluates and compares the finite-sample performance of the competing estimators. The practical usefulness of the proposed model is illustrated through two real directional datasets involving sun compass orientation measurements of starhead topminnows and wind direction observations. Comparisons with several established circular models indicate that the WQL distribution provides competitive fitting performance for the considered datasets. We discuss its parsimonious structure and analytical tractability, along with the implications of its structural discontinuity at the wrap point, in the context of directional data analysis.
Related
- Statistical inference and applications of Kumaraswamy Odd Perks power Lomax distribution
- The LR1 Lifetime Distribution: Properties, Nonmonotone Hazard, and Statistical Inference
- The Topp-Leone XLindley Distribution: Properties, Estimation and Applications to Lifetime Data
- Reliability Modeling using an Equilibrium-Based Xgamma Distribution: Properties, Estimation, and Applications
- A Flexible Extension of the Power Function Distribution: Properties and Applications
BibTeX
@article{phookan2026wrapped,
title = {{The Wrapped Q-Lindley Distribution: A New Circular Model with Statistical Properties, Classical and Bayesian Inference, and Applications to Directional Data}},
author = {Swapnil Swagat Phookan and Sajadul Hussain and Partha Jyoti Hazarika and Diego I. Gallardo and Osvaldo Venegas},
journal = {Axioms},
year = {2026},
month = oct,
doi = {10.3390/axioms15100754},
url = {https://www.mdpi.com/2075-1680/15/10/754},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - The Wrapped Q-Lindley Distribution: A New Circular Model with Statistical Properties, Classical and Bayesian Inference, and Applications to Directional Data
AU - Swapnil Swagat Phookan
AU - Sajadul Hussain
AU - Partha Jyoti Hazarika
AU - Diego I. Gallardo
AU - Osvaldo Venegas
PY - 2026
DA - 2026/10/10
JO - Axioms
DO - 10.3390/axioms15100754
UR - https://www.mdpi.com/2075-1680/15/10/754
AB - Circular data arise naturally in a wide range of scientific fields, including biology, geology, meteorology, and environmental sciences, where conventional linear statistical methods are inappropriate unless the circular structure of the observations is taken into account. Motivated by the need for parsimonious, analytically tractable models for unimodal directional data, we introduce a new one-parameter circular model, the Wrapped Q-Lindley (WQL) distribution. The proposed model is obtained by wrapping the Q-Lindley distribution and has a specific unimodal asymmetric shape. Closed-form or analytically tractable expressions are derived for several important distributional properties, including the characteristic function, trigonometric moments, circular descriptive measures, and Rényi entropy. We investigate parameter estimation using ten classical estimation methods, along with Bayesian inference, under four symmetric and asymmetric loss functions. A Monte Carlo simulation study evaluates and compares the finite-sample performance of the competing estimators. The practical usefulness of the proposed model is illustrated through two real directional datasets involving sun compass orientation measurements of starhead topminnows and wind direction observations. Comparisons with several established circular models indicate that the WQL distribution provides competitive fitting performance for the considered datasets. We discuss its parsimonious structure and analytical tractability, along with the implications of its structural discontinuity at the wrap point, in the context of directional data analysis.
SN - 2075-1680
ER -