Estimating the parameter of an exponential distribution based on multiply progressive censored competing risks data†
Kyeongjun Lee1
1Department of Mathematics and Big Data Science, Kumoh National Institute of Technology
Correspondence to: † This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (NRF-2022R1I1A3068582).
1 Assistant professor, Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, Gumi 39177, Korea. E-mail: indra_74@naver.com
1 Assistant professor, Department of Mathematics and Big Data Science, Kumoh National Institute of Technology, Gumi 39177, Korea. E-mail: indra_74@naver.com
Received April 30, 2024; Revised May 20, 2024; Accepted May 21, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- There are many situation in life testing experiments in which units are lost or removed from experimentation before failure. Therefore, multiply progressive censoring scheme was introduced. In lifetime data analysis, moreover, it is generally known that more than one cause or risk factor may be present at the same time. In this paper, therefore, we propose the estimators of the parameter and uncertainty measure of the exponential distribution under multiply progressive censored competing risk data. First, we derive the MLE for the parameter and uncertainty measure of exponential distribution. And we derive the Bayesian estimators for the parameter and uncertainty measure of exponential distribution under squared error loss function (SEL), precautionary loss function (PLF) and DeGroot loss function (DLF). We also compare the proposed estimators in the sense of the mean squared error (MSE) and bias under various multiply progressive censoring scheme. Finally, the validity of the proposed methods are demonstrated by a real data.
- Keywords : Bayesian estimation, exponential distribuiton, multiply progressive censoring, uncertainty measure
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