A generalized Lindley distribution:Properties, estimation and applications under progressively type-Ⅱ censored samples

Haiping Ren; Jiajie Shi; Haiping Ren; Jiajie Shi

doi:10.3934/math.2025480

AIMS Mathematics

2025, Volume 10, Issue 5: 10554-10590. doi: 10.3934/math.2025480

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A generalized Lindley distribution:Properties, estimation and applications under progressively type-Ⅱ censored samples

Haiping Ren ^{1
,
,},
Jiajie Shi ²

1.
Teaching Department of Basic Subjects, Jiangxi University of Science and Technology, Nanchang, 330013, China
2.
College of Science, Jiangxi University of Science and Technology, Ganzhou, 341000, China

Received: 27 February 2025 Revised: 10 April 2025 Accepted: 15 April 2025 Published: 08 May 2025
MSC : 62E10; 62F10

A two-parameter generalized Lindley distribution is proposed, whose probability density function contains two models that are particularly well-suited for lifetime studies: the inverted J-type and the unimodal left-leaning type. Some of the main numerical characteristics of the proposed distribution were investigated. Additionally, based on progressively type-Ⅱ censored samples, three estimation methods were used to estimate the parameters, reliability function, and hazard function of the distribution: maximum product spacing estimation, maximum likelihood estimation, and Bayesian estimation. Bayesian estimators were obtained under squared error and general entropy loss functions, and the Metropolis-Hastings algorithm was used to obtain Bayesian estimates. In addition to point estimation, corresponding asymptotic confidence intervals and the highest posterior density intervals were also studied. Through Monte Carlo simulation, we measured the performance of the three estimators using four criteria. Finally, the ability of the proposed distribution to accurately fit the data was demonstrated using a real dataset.
Citation: Haiping Ren, Jiajie Shi. A generalized Lindley distribution:Properties, estimation and applications under progressively type-Ⅱ censored samples[J]. AIMS Mathematics, 2025, 10(5): 10554-10590. doi: 10.3934/math.2025480

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Abstract

A two-parameter generalized Lindley distribution is proposed, whose probability density function contains two models that are particularly well-suited for lifetime studies: the inverted J-type and the unimodal left-leaning type. Some of the main numerical characteristics of the proposed distribution were investigated. Additionally, based on progressively type-Ⅱ censored samples, three estimation methods were used to estimate the parameters, reliability function, and hazard function of the distribution: maximum product spacing estimation, maximum likelihood estimation, and Bayesian estimation. Bayesian estimators were obtained under squared error and general entropy loss functions, and the Metropolis-Hastings algorithm was used to obtain Bayesian estimates. In addition to point estimation, corresponding asymptotic confidence intervals and the highest posterior density intervals were also studied. Through Monte Carlo simulation, we measured the performance of the three estimators using four criteria. Finally, the ability of the proposed distribution to accurately fit the data was demonstrated using a real dataset.

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