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Order-Restricted Inference for Generalized Inverted Exponential Distribution under Balanced Joint Progressive Type-II Censored Data and Its Application on the Breaking Strength of Jute Fibers

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  • Chunmei Zhang

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China)

  • Tao Cong

    (Metals & Chemistry Research Institute, China Academy of Railway Sciences Corporation Limited, Beijing 100081, China)

  • Wenhao Gui

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

This article considers a new improved balanced joint progressive type-II censoring scheme based on two different populations, where the lifetime distributions of two populations follow the generalized inverted exponential distribution with different shape parameters but a common scale parameter. The maximum likelihood estimates of all unknown parameters are obtained and their asymptotic confidence intervals are constructed by the observed Fisher information matrix. Furthermore, the existence and uniqueness of solutions are proved. In the Bayesian framework, the common scale parameter follows an independent Gamma prior and the different shape parameters jointly follow a Beta-Gamma prior. Based on whether the order restriction is imposed on the shape parameters, the Bayesian estimates of all parameters concerning the squared error loss function along with the associated highest posterior density credible intervals are derived by using the importance sampling technique. Then, we use Monte Carlo simulations to study the performance of the various estimators and a real dataset is discussed to illustrate all of the estimation techniques. Finally, we seek an optimum censoring scheme through different optimality criteria.

Suggested Citation

  • Chunmei Zhang & Tao Cong & Wenhao Gui, 2023. "Order-Restricted Inference for Generalized Inverted Exponential Distribution under Balanced Joint Progressive Type-II Censored Data and Its Application on the Breaking Strength of Jute Fibers," Mathematics, MDPI, vol. 11(2), pages 1-26, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:329-:d:1029042
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    References listed on IDEAS

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    1. Rajni Goel & Hare Krishna, 2022. "Statistical inference for two Lindley populations under balanced joint progressive type-II censoring scheme," Computational Statistics, Springer, vol. 37(1), pages 263-286, March.
    2. Shuvashree Mondal & Debasis Kundu, 2019. "Point and Interval Estimation of Weibull Parameters Based on Joint Progressively Censored Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-25, June.
    3. 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.
    4. Balakrishnan, N. & Rasouli, Abbas, 2008. "Exact likelihood inference for two exponential populations under joint Type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2725-2738, January.
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