Estimation of exponentiated Nadarajah-Haghighi distribution under progressively type-II censored sample with application to bladder cancer data


In this article we consider statistical inferences about the unknown parameters of the exponentiated Nadarajah-Haghighi (ENH) distribution based on progressively type-II censoring using classical and Bayesian procedures. For classical procedures, maximum likelihood (ML) and least square estimators of the unknown parameters are derived. The Bayes estimators are obtained based on both the symmetric (squared error) and asymmetric (LINEX, general entropy) loss functions. Furthermore, Markov chain Monte Carlo (MCMC) technique is used to compute the Bayes estimators and the associated credible intervals. Moreover, asymptotic confidence intervals are constructed using the normality property of the ML estimates. After that, the asymptotic confidence intervals using ML estimates and two parametric bootstrap confidence intervals are provided to compare with Bayes credible intervals. Finally, simulation study and a bladder cancer application are presented to illustrate the proposed methods of estimation.


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The authors would like to thank the Editor and reviewers for their valuable comments and suggestions to improve the presentation of the paper. The authors would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project No. 1440-142.

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Correspondence to Ziyad A. Alhussain or Essam A. Ahmed.

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Alhussain, Z.A., Ahmed, E.A. Estimation of exponentiated Nadarajah-Haghighi distribution under progressively type-II censored sample with application to bladder cancer data. Indian J Pure Appl Math 51, 631–657 (2020).

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Key words

  • Exponentiated Nadarajah-Haghighi distribution
  • maximum likelihood estimators
  • least squares estimators
  • Bayes estimators
  • bootstrap
  • Markov chain Monte Carlo

2010 Mathematics Subject Classification

  • 62F05
  • 62F10
  • 62F15
  • 62F40
  • 65C40