On a Mixture of the Lindley and Modified Lindley Distributions: Properties and Estimation

Title

On a Mixture of the Lindley and Modified Lindley Distributions: Properties and Estimation

Creator

Chesneau, Christophe; Tomy, Lishamol; Gillariose, Jiju

Description

In this article, we investigate a novel three-parameter lifetime distribution constructed from a mixture of the original Lindley and modified Lindley distributions. The concept behind this construction is to combine the contrasting properties of these two well-known distributions to provide a new statistical modeling option for lifetime data analysis. In particular, it provides a natural alternative to the three-parameter, two-component mixture of the Lindley distribution, which has attracted attention in the recent statistical literature. We investigate its main properties from both a theoretical and practical point of view. The shapes of the corresponding probability density and hazard rate functions and the formulas for the moments, moment generating functions and characteristic functions are discussed. The distribution is then subjected to statistical analysis, considering it as a semi-parametric model. The maximum likelihood approach is used to estimate the parameters. In a simulation analysis, the numerical behavior of the bias and the mean square error of the obtained estimates are studied. The new model is tested on three data sets and the results show that it has a better fit behavior than its main competitor, the three-parameter two-component mixture of the Lindley model. 2025 YU

Source

Jordan Journal of Mathematics and Statistics;Volume;18;Issue;3;pp.473-486

Date

01-01-2025

Publisher

Yarmouk University

Subject

Lindley distributions; maximum likelihood estimates; mixture distribution; modified Lindley distribution; moments

Coverage

Chesneau C., Universitde Caen, LMNO, Campus II, Science 3, Caen, 14032, France; Tomy L., Department of Statistics, Deva Matha College, Kerala, Kuravilangad, 686633, India; Gillariose J., Department of Statistics and Data Science, Christ University, Karnataka, Bangalore, 560029, India

Rights

Restricted Access; Hardcopy may be available in the library

Relation

ISSN: 20757905;

Format

online

Language

English

Type

Article

Identifier

https://doi.org/10.47013/18.3.13

https://www.scopus.com/pages/publications/105030515803?origin=resultslist