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Estimation and prediction for a new Pareto-type distribution under progressive type-II censoring

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  • Saadati Nik, A.
  • Asgharzadeh, A.
  • Raqab, Mohammad Z.

Abstract

In this paper, we consider the problems of estimating the unknown parameters as well as predicting the failure times of the removed units in multiple stages of the progressively censored sample coming from a new Pareto-type distribution. First, maximum likelihood, least squares and Bayesian methods (Lindley’s approximation and Markov chain Monte Carlo) are applied for estimating the parameters involved in this model. For predicting the failure times of the removed units, different prediction methods including maximum likelihood, best unbiased, conditional median and Bayesian prediction methods are adopted. We also develop prediction intervals of future lifetimes using pivot and highest conditional density methods. Comprehensive Monte Carlo simulations are performed to assess the performance of the estimation methods as well as prediction methods. Finally, analysis of a real data set representing the duration of remission of leukemia patients who were treated by a specific drug is performed for illustration purposes.

Suggested Citation

  • Saadati Nik, A. & Asgharzadeh, A. & Raqab, Mohammad Z., 2021. "Estimation and prediction for a new Pareto-type distribution under progressive type-II censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 508-530.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:508-530
    DOI: 10.1016/j.matcom.2021.06.005
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    References listed on IDEAS

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    1. Jazaa S. Al-Mutairi & Mohammad Z. Raqab, 2020. "Confidence intervals for quantiles based on samples of random sizes," Statistical Papers, Springer, vol. 61(1), pages 261-277, February.
    2. Basak, Indrani & Basak, Prasanta & Balakrishnan, N., 2006. "On some predictors of times to failure of censored items in progressively censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1313-1337, March.
    3. Kotb, M.S. & Raqab, M.Z., 2019. "Statistical inference for modified Weibull distribution based on progressively type-II censored data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 233-248.
    4. Gunasekera, Sumith, 2018. "Inference for the Burr XII reliability under progressive censoring with random removals," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 182-195.
    5. Raqab, Mohammad Z. & Asgharzadeh, A. & Valiollahi, R., 2010. "Prediction for Pareto distribution based on progressively Type-II censored samples," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1732-1743, July.
    6. Krishna, Hare & Kumar, Kapil, 2011. "Reliability estimation in Lindley distribution with progressively type II right censored sample," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 281-294.
    7. Bourguignon, Marcelo & Saulo, Helton & Fernandez, Rodrigo Nobre, 2016. "A new Pareto-type distribution with applications in reliability and income data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 166-175.
    8. Ali Saadati Nik & Akbar Asgharzadeh & Saralees Nadarajah, 2019. "Comparisons of Methods of Estimation for a New Pareto-type Distribution," Statistica, Department of Statistics, University of Bologna, vol. 79(3), pages 291-319.
    9. Valiollahi, R. & Raqab, Mohammad Z. & Asgharzadeh, A. & Alqallaf, F.A., 2018. "Estimation and prediction for power Lindley distribution under progressively type II right censored samples," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 32-47.
    10. Essam Al-Hussaini & Abd Ahmad, 2003. "On Bayesian interval prediction of future records," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 79-99, June.
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