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Annals of Data Science

, Volume 6, Issue 4, pp 673–705 | Cite as

Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data

  • M. M. Mohie El-Din
  • M. Nagy
  • M. H. Abu-MoussaEmail author
Article
  • 92 Downloads

Abstract

In this paper, the statistical inference for the Gompertz distribution based on generalized progressively hybrid censored data is discussed. The estimation of the parameters for Gompertz distribution is discussed using the maximum likelihood method and the Bayesian methods under different loss functions. The existence and uniqueness of the maximum likelihood estimation are proved. The point and interval Bayesian predictions for unobserved failures from the same sample and that from the future sample are derived. The Monte Carlo simulation is applied to compare the proposed methods. A real data example is used to apply the methods of estimation and to construct the prediction intervals.

Keywords

Bayesian estimation Generalized progressive hyprid censored samples Gompertz distribution Maximum likelihood estimation Bayesian prediction intervals 

Mathematics Subject Classification

Primary 62G30 Secondary 62F15 

Notes

Acknowledgements

This project was supported by King Saud University, Deanship of Scientific Research, College of Science Research Center. The authors are sincerely grateful to the referees and to the Editor-in-Chief for their many constructive comments and careful reading of the paper.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • M. M. Mohie El-Din
    • 1
  • M. Nagy
    • 2
    • 3
  • M. H. Abu-Moussa
    • 4
    Email author
  1. 1.Department of Mathematics, Faculty of ScienceAl-Azhar UniversityCairoEgypt
  2. 2.Department of Statistics and Operation Reseach, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  3. 3.Department of Mathematics, Faculty of ScienceFayoum UniversityFayoumEgypt
  4. 4.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt

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