Estimations of competing lifetime data from inverse Weibull distribution under adaptive progressively hybrid censored

Wael S. Abu El Azm; Ramy Aldallal; Hassan M. Aljohani; Said G. Nassr; Wael S. Abu El Azm; Ramy Aldallal; Hassan M. Aljohani; Said G. Nassr

doi:10.3934/mbe.2022292

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 6: 6252-6275. doi: 10.3934/mbe.2022292

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Estimations of competing lifetime data from inverse Weibull distribution under adaptive progressively hybrid censored

1.
Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt
2.
College of Business Administration in Hotat bani Tamim, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
3.
Department of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
4.
Faculty of Business Administration, Sinai University, Al-Arish 45511, Egypt

Academic Editor: Jeffrey Yi-Lin Forrest

Received: 04 January 2022 Accepted: 06 March 2022 Published: 18 April 2022

In real-life experiments, collecting complete data is time-, finance-, and resources-consuming as stated by statisticians and analysts. Their goal was to compromise between the total time of testing, the number of units under scrutiny, and the expenditures paid through a censoring scheme. Comparing failure-censored schemes (Type-Ⅱ and Progressive Type-Ⅱ) to Time-censored schemes (Type-Ⅰ), it's worth noting that the former is time-consuming and is no more suitable to be applied in real-life situations. This is the reason why the Type-Ⅰ adaptive progressive hybrid censoring scheme has exceeded other failure-censored types; Time-censored types enable analysts to accomplish their trials and experiments in a shorter time and with higher efficiency. In this paper, the parameters of the inverse Weibull distribution are estimated under the Type-Ⅰ adaptive progressive hybrid censoring scheme (Type-Ⅰ APHCS) based on competing risks data. The model parameters are estimated using maximum likelihood estimation and Bayesian estimation methods. Further, we examine the asymptotic confidence intervals and bootstrap confidence intervals for the unknown model parameters. Monte Carlo simulations are carried out to compare the performance of the suggested estimation methods under Type-Ⅰ APHCS. Moreover, Markov Chain Monte Carlo by applying Metropolis-Hasting algorithm under the square error of loss function is used to compute Bayes estimates and related to the highest posterior density. Finally, two data sets are studied to illustrate the introduced methods of inference. Based on our results, we can conclude that the Bayesian estimation outperforms the maximum likelihood estimation for estimating the inverse Weibull parameters under Type-Ⅰ APHCS.
- Competing risks,
- type-Ⅰ adaptive progressive hybrid censoring scheme,
- maximum likelihood estimation,
- bootstrap confidence intervals,
- Bayesian estimation,
- MCMC approach
Citation: Wael S. Abu El Azm, Ramy Aldallal, Hassan M. Aljohani, Said G. Nassr. Estimations of competing lifetime data from inverse Weibull distribution under adaptive progressively hybrid censored[J]. Mathematical Biosciences and Engineering, 2022, 19(6): 6252-6275. doi: 10.3934/mbe.2022292

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Abstract

In real-life experiments, collecting complete data is time-, finance-, and resources-consuming as stated by statisticians and analysts. Their goal was to compromise between the total time of testing, the number of units under scrutiny, and the expenditures paid through a censoring scheme. Comparing failure-censored schemes (Type-Ⅱ and Progressive Type-Ⅱ) to Time-censored schemes (Type-Ⅰ), it's worth noting that the former is time-consuming and is no more suitable to be applied in real-life situations. This is the reason why the Type-Ⅰ adaptive progressive hybrid censoring scheme has exceeded other failure-censored types; Time-censored types enable analysts to accomplish their trials and experiments in a shorter time and with higher efficiency. In this paper, the parameters of the inverse Weibull distribution are estimated under the Type-Ⅰ adaptive progressive hybrid censoring scheme (Type-Ⅰ APHCS) based on competing risks data. The model parameters are estimated using maximum likelihood estimation and Bayesian estimation methods. Further, we examine the asymptotic confidence intervals and bootstrap confidence intervals for the unknown model parameters. Monte Carlo simulations are carried out to compare the performance of the suggested estimation methods under Type-Ⅰ APHCS. Moreover, Markov Chain Monte Carlo by applying Metropolis-Hasting algorithm under the square error of loss function is used to compute Bayes estimates and related to the highest posterior density. Finally, two data sets are studied to illustrate the introduced methods of inference. Based on our results, we can conclude that the Bayesian estimation outperforms the maximum likelihood estimation for estimating the inverse Weibull parameters under Type-Ⅰ APHCS.

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