Abstract
In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.
Highlights
In life testing and reliability analysis, some units can be lost or withdrawn from the experiment before failure occurs
One of the major reasons for removal of the experimental units is to save the working experimental units for future use, thereby conserving the cost and time associated with testing. is leads us to use the censoring schemes. e type-II censoring can be considered a common type of censored scheme
Many authors have studied the statistical inference for different probability distributions using progressive type-II censoring, including Balakrishnan and Sandhu [1, 2], Cohen [3], Mann [4], Ng [5], Balakrishnan et al [6], Gibbons and Vance [7], Yuen and Tse [8], Ng et al [9], Balakrishnan [10], Soliman [11, 12], Madi and Raqab [13], Mahmoud et al [14], Mahmoud et al [15], Soliman et al [16], El-Sagheer [17,18,19], Mahmoud et al [20], ElSagheer and Hasaballah [21], El-Sagheer et al [22], and Soliman et al [23]
Summary
In life testing and reliability analysis, some units can be lost or withdrawn from the experiment before failure occurs. For more details about statistical inference using first-failure censoring, it is recommended that the reader refers to Wu and Yu [26], Wu et al [27], Lee et al [28], and Wu et al [29] Using this censoring scheme does not enable the experimenter to remove experimental units from the test until the first failure is observed. Generalized Pareto distribution (GPD) is a significant continuous lifetime distribution It plays a key role in statistical inference studies and reliability problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
