Abstract
In this paper, we consider Chen distribution and derive UMVUEs and MLEs of the parameter λ , hazard rate h(t) and the two measures of reliability, namely R(t) = P(X > t), where X denotes the lifetime of an item and P = P(X > Y ), which represents the reliability of an item or system of random strength X subject to random stress Y , under type II censoring scheme and the sampling scheme of Bartholomew . We also develop interval estimates of the reliability measures. Testing procedures for the hypotheses related to different parametric functions have also been developed. A comparative study of different methods of point estimation and average confiddence length has been done through simulation studies. The analysis of a real data set is presented for illustration purpose.
Highlights
In the reliability literature, we have many such distributions whose hazard rate functions are constant, increasing or decreasing in nature
The paper is organized as follows: In Section 2, we provide MLEs and UMVUEs of parameter λq, hazard rate h(t) and the reliability functions R(t) and P based on type II censoring scheme assuming β to be known
For t = 1 and beyond, the performance of MLE is better than UMVUE
Summary
We have many such distributions (e.g. generalized exponential, gamma, Weibull and lognormal) whose hazard rate functions are constant, increasing or decreasing in nature These are the most commonly used models and we analyze various real life phenomenon using them. [2] obtained Empirical Bayes estimators of the scale parameter, reliability and hazard rate functions of Chen distribution under the condition when a sample is obtained from a type-I censoring scheme. The paper is organized as follows: In Section 2, we provide MLEs and UMVUEs of parameter λq, hazard rate h(t) and the reliability functions R(t) and P based on type II censoring scheme assuming β to be known. Proofs of some important results can be found in the Appendix
Sign-in/Register to view highlights & summary 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 callMore From: Statistics, Optimization & Information Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
