Statistical inference for the Power Rayleigh distribution based on adaptive progressive Type-II censored data

Hatim Solayman Migdadi; Nesreen M. Al-Olaimat; Maryam Mohiuddin; Omar Meqdadi; Hatim Solayman Migdadi; Nesreen M. Al-Olaimat; Maryam Mohiuddin; Omar Meqdadi

doi:10.3934/math.20231149

AIMS Mathematics

2023, Volume 8, Issue 10: 22553-22576. doi: 10.3934/math.20231149

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Research article

Statistical inference for the Power Rayleigh distribution based on adaptive progressive Type-II censored data

1.
Department of Mathematics, Faculty of Science, The Hashemite University, Zarqa 13133, Jordan
2.
Department of Mathematics, Faculty of Science, Ajloun National University, Ajloun 26810, Jordan
3.
Department of mathematics, Faculty of science, National Institute of Technology Calicut, Kerla, India
4.
Department of mathematics, Faculty of science, Jordan university of science and technology, Irbid 22110, Jordan

Received: 18 May 2023 Revised: 29 June 2023 Accepted: 04 July 2023 Published: 17 July 2023
MSC : 62F10, 62F15, 62N01, 62N02, 62N05

The Power Rayleigh distribution (PRD) is a new extension of the standard one-parameter Rayleigh distribution. To employ this distribution as a life model in the analysis of reliability and survival data, we focused on the statistical inference for the parameters of the PRD under the adaptive Type-II censored scheme. Point and interval estimates for the model parameters and the corresponding reliability function at a given time are obtained using likelihood, Bootstrap and Bayesian estimation methods. A simulation study is conducted in different settings of the life testing experiment to compare and evaluate the performance of the estimates obtained. In addition, the estimation procedure is also investigated in real lifetimes data. The results indicated that the obtained estimates gave an accurate and efficient estimation of the model parameters. The Bootstrap estimates are better than the estimates obtained by the likelihood estimation approach, and estimates obtained using the Markov Chain Monte Carlo method by the Bayesian approach under both the squared error and the general entropy loss functions have priority over other point and interval estimates. Under the adaptive Type-II censoring scheme, concluding results confirmed that the PRD can be effectively used to model the lifetimes in survival and reliability analysis.
- Power Rayleigh distribution,
- adaptive Type-II censored scheme,
- maximum likelihood estimation,
- Bayesian estimation,
- Bootstrap estimation
Citation: Hatim Solayman Migdadi, Nesreen M. Al-Olaimat, Maryam Mohiuddin, Omar Meqdadi. Statistical inference for the Power Rayleigh distribution based on adaptive progressive Type-II censored data[J]. AIMS Mathematics, 2023, 8(10): 22553-22576. doi: 10.3934/math.20231149

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Abstract

The Power Rayleigh distribution (PRD) is a new extension of the standard one-parameter Rayleigh distribution. To employ this distribution as a life model in the analysis of reliability and survival data, we focused on the statistical inference for the parameters of the PRD under the adaptive Type-II censored scheme. Point and interval estimates for the model parameters and the corresponding reliability function at a given time are obtained using likelihood, Bootstrap and Bayesian estimation methods. A simulation study is conducted in different settings of the life testing experiment to compare and evaluate the performance of the estimates obtained. In addition, the estimation procedure is also investigated in real lifetimes data. The results indicated that the obtained estimates gave an accurate and efficient estimation of the model parameters. The Bootstrap estimates are better than the estimates obtained by the likelihood estimation approach, and estimates obtained using the Markov Chain Monte Carlo method by the Bayesian approach under both the squared error and the general entropy loss functions have priority over other point and interval estimates. Under the adaptive Type-II censoring scheme, concluding results confirmed that the PRD can be effectively used to model the lifetimes in survival and reliability analysis.

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