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Inferences and Optimal Censoring Schemes for Progressively First-Failure Censored Nadarajah-Haghighi Distribution

Author

Listed:
  • Samir K. Ashour

    (Institute of Statistical Studies and Research, Cairo University)

  • Ahmed A. El-Sheikh

    (Institute of Statistical Studies and Research, Cairo University)

  • Ahmed Elshahhat

    (Zagazig University)

Abstract

A new extension of the exponential distribution, proposed by Nadarajah and Haghighi (Statistics 45, 543–558 (2011)), is an alternative to the gamma, Weibull and generalized-exponential models, it is also known as NH distribution. The maximum likelihood and Bayes inferential approaches for estimating the unknown two-parameters and some lifetime parameters such as survival and hazard rate functions of the NH distribution in presence of progressive first-failure censored sampling are considered. Based on observed Fisher’s information matrix, the approximate confidence intervals for the two-parameters, and any function of them, are constructed. Using Lindley’s approximation and Markov chain Monte Carlo methods under the assumption of conjugate gamma priors, the Bayes estimates and associate highest posterior density credible intervals for the unknown parameters and reliability characteristics are developed based on squared error loss function. Although the proposed estimators cannot be expressed in explicit forms, these can be easily obtained through the use of appropriate numerical techniques. A Monte Carlo simulation study is carried out to examine the performance of proposed methods. Using different optimality criteria, an optimal censoring scheme has been suggested. Finally, a real data set is analyzed for illustration purposes.

Suggested Citation

  • Samir K. Ashour & Ahmed A. El-Sheikh & Ahmed Elshahhat, 2022. "Inferences and Optimal Censoring Schemes for Progressively First-Failure Censored Nadarajah-Haghighi Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 885-923, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-019-00175-2
    DOI: 10.1007/s13171-019-00175-2
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    References listed on IDEAS

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    1. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    2. Wu, Shuo-Jye & Kus, Coskun, 2009. "On estimation based on progressive first-failure-censored sampling," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3659-3670, August.
    3. Tanmay Sen & Yogesh Mani Tripathi & Ritwik Bhattacharya, 2018. "Statistical Inference and Optimum Life Testing Plans Under Type-II Hybrid Censoring Scheme," Annals of Data Science, Springer, vol. 5(4), pages 679-708, December.
    4. Sanku Dey & Chunfang Zhang & A. Asgharzadeh & M. Ghorbannezhad, 2017. "Comparisons of Methods of Estimation for the NH Distribution," Annals of Data Science, Springer, vol. 4(4), pages 441-455, December.
    5. Biswabrata Pradhan & Debasis Kundu, 2009. "On progressively censored generalized exponential distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 497-515, November.
    6. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
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    Cited by:

    1. Ahmed Elshahhat & Osama E. Abo-Kasem & Heba S. Mohammed, 2023. "Survival Analysis of the PRC Model from Adaptive Progressively Hybrid Type-II Censoring and Its Engineering Applications," Mathematics, MDPI, vol. 11(14), pages 1-26, July.
    2. Ahmed Elshahhat & Refah Alotaibi & Mazen Nassar, 2022. "Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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