A Lambert-Type Lindley Distribution as an Alternative for Skewed Unimodal Positive Data

Daniel H. Castañeda, Isaac Cortés and Yuri A. Iriarte ()
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Daniel H. Castañeda: Escuela de Postgrado, Universidad de Antofagasta, Antofagasta 1240000, Chile
Isaac Cortés: Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 7820436, Chile
Yuri A. Iriarte: Departamento de Estadística y Ciencia de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2025, vol. 13, issue 21, 1-20

Abstract: This paper introduces the Lambert-Lindley distribution, a two-parameter extension of the Lindley model constructed through the Lambert- F generator. The new distribution retains the non-negative support of the Lindley distribution and provides additional flexibility by incorporating a shape parameter that controls skewness and tail behavior. Structural properties are derived, including the probability density function, cumulative distribution function, quantile function, hazard rate, and moments. Parameter estimation is addressed using the method of moments and maximum likelihood, and a Monte Carlo simulation study carried out to evaluate the performance of the proposed estimators. The practical applicability of the Lambert–Lindley distribution is demonstrated with two real datasets: stress rupture times of Kevlar/epoxy composites and hospital stay durations of breast cancer patients. Comparative analyses using goodness-of-fit tests and information criteria demonstrate that the proposed model can outperform classical alternatives such as the Gamma and Weibull distributions. Consequently, the Lambert–Lindley distribution emerges as a flexible alternative for modeling positive unimodal data in contexts such as material reliability studies and clinical duration analysis.

Keywords: Lindley distribution; Lambert-F generator; reliability analysis; maximum likelihood estimation; Monte Carlo simulation; positive data modeling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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