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

Chunmei Zhang, Tao Cong and Wenhao Gui ()
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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

Mathematics, 2023, vol. 11, issue 2, 1-26

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.

Keywords: generalized inverted exponential distribution; maximum likelihood estimation; optimum censoring scheme; balanced joint progressive censoring; Bayesian estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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