On an extension of the two-parameter Lindley distribution

Title

On an extension of the two-parameter Lindley distribution

Creator

Gillariose J.; Tomy L.

Description

AIM: Lindley distribution has been widely studied in statistical literature because it accommodates several interesting properties. In lifetime data analysis contexts, Lindley distribution gives a good description over exponential distribution. It has been used for analysing copious real data sets, specifically in applications of modeling stress-strength reliability. This paper proposes a new generalized two-parameter Lindley distribution and provides a comprehensive description of its statistical properties such as order statistics, limiting distributions of order statistics, Information theory measures, etc. METHODS: We study shapes of the probability density and hazard rate functions, quantiles, moments, moment generating function, order statistic, limiting distributions of order statistics, information theory measures, and autoregressive models are among the key characteristics and properties discussed. The two-parameter Lindley distribution is then subjected to statistical analysis. The paper uses methods of maximum likelihood to estimate the parameters of the proposed distribution. The usefulness of the proposed distribution for modeling data is illustrated using a real data set by comparison with other generalizations of the exponential and Lindley distributions and is depicted graphically. RESULTS/FINDINGS: This paper presents relevant characteristics of the proposed distribution and applications. Based on this study, we found that the proposed model can be used quite effectively to analyzing lifetime data. CONCLUSIONS: In this article, we proffered a new customized Lindley distribution. The proposed distribution enfolds exponential and Lindley distributions as sub-models. Some properties of this distribution such as quantile function, moments, moment generating function, distributions of order statistics, limiting distributions of order statistics, entropy, and autoregressive time series models are studied. This distribution is found to be the most appropriate model to fit the carbon fibers data compared to other models. Consequently, we propose the MOTL distribution for sketching inscrutable lifetime data sets. 2023 DSR Publishers/The University of Jordan.

Source

Reliability: Theory and Applications, Vol-18, No. 1, pp. 385-402.

Date

2023-01-01

Publisher

Gnedenko Forum

Subject

Exponential distribution; Generalized family; Lindley distribution; Marshall-Olkin extended distribution; Maximum likelihood estimation

Coverage

Gillariose J., Department of Statistics, CHRIST (Deemed to Be University), Karnataka, Bangalore, 560029, India; Tomy L., Department of Statistics, Deva Matha College, Kerala, Kuravilangad, 686633, India

Rights

Restricted Access

Relation

ISSN: 19322321

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.24412/1932-2321-2023-172-385-402

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