Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II progressive censoring data

Manal M. Yousef; Rehab Alsultan; Said G. Nassr; Manal M. Yousef; Rehab Alsultan; Said G. Nassr

doi:10.3934/mbe.2023076

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 1674-1694. doi: 10.3934/mbe.2023076

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Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II progressive censoring data

1.
Department of Mathematics, Faculty of Science, New Valley University, El-Khargah 72511, Egypt
2.
Department of Mathematical Science, Faculty of Applied Science, Umm AL-Qura University, Makkah 24382, Saudi Arabia
3.
Department of Statistics and Insurance, Faculty of Commerce, Arish University, Egypt
4.
Higher Institute for Administrative Sciences, Belbis, El-Sharquia, Egypt

Academic Editor: Jeffrey Yi-Lin Forrest

Received: 21 June 2022 Revised: 16 October 2022 Accepted: 24 October 2022 Published: 04 November 2022

This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice.
Citation: Manal M. Yousef, Rehab Alsultan, Said G. Nassr. Parametric inference on partially accelerated life testing for the inverted Kumaraswamy distribution based on Type-II progressive censoring data[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 1674-1694. doi: 10.3934/mbe.2023076

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Abstract

This article discusses the problem of estimation with step stress partially accelerated life tests using Type-II progressively censored samples. The lifetime of items under use condition follows the two-parameters inverted Kumaraswamy distribution. The maximum likelihood estimates for the unknown parameters are computed numerically. Using the property of asymptotic distributions for maximum likelihood estimation, we constructed asymptotic interval estimates. The Bayes procedure is used to calculate estimates of the unknown parameters from symmetrical and asymmetric loss functions. The Bayes estimates cannot be obtained explicitly, therefor the Lindley's approximation and the Markov chain Monte Carlo technique are used to obtaining the Bayes estimates. Furthermore, the highest posterior density credible intervals for the unknown parameters are calculated. An example is presented to illustrate the methods of inference. Finally, a numerical example of March precipitation (in inches) in Minneapolis failure times in the real world is provided to illustrate how the approaches will perform in practice.

References

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