E-Bayesian inference for xgamma distribution under progressive type II censoring with binomial removals and their applications

ABSTRACT

In this article, we propose E-Bayes estimators of the parameter of xgamma distribution under squared error loss function, general entropy loss function, and linear exponential loss function for progressive type II censored data with binomial removals. The proposed estimators, maximum likelihood estimator, and corresponding Bayes estimators are compared in terms of their risks based on simulated samples from xgamma distribution. The proposed methodology is illustrated on two real data sets of bile duct cancer data and the endurance of deep-groove ball bearings data.

KEYWORDS:

• xgamma
• PT II CBRs
• MLE
• bootstrap
• E-Bayes inference

Acknowledgments

The authors wish to thank the Editor-in-Chief Jie Shen and the referees for their valuable and fruitful comments and suggestions without which the article could not have taken its present form.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Ethical approval

This article does not contain any studies with human participants and animal participants performed by any of the authors.

Additional information

Notes on contributors

Anurag Pathak

Anurag Pathak received his Ph.D. (Statistics) in June 2022 from Central University of Haryana, India. His current research interests include lifetime analysis, ecological modeling, Bayesian inference, and epidemiological study. He has published a number of research articles.

Manoj Kumar

Manoj Kumar, Ph.D., currently works as an Assistant Professor at the Central University of Haryana, Mahendergarh, Haryana, India. His area of research interests include lifetime analysis, ecological modeling, and Bayesian inference. Also, he published a number of research articles and reviewed several articles from various journals.

Sanjay Kumar Singh

Sanjay Kumar Singh, Ph.D., currently works as a Professor and Head of Department (Statistics) at Banaras Hindu University, Varanasi, India. His research area includes lifetime analysis, ecological modeling, and Bayesian Inference.

Umesh Singh

Umesh Singh, Ph.D., is currently working as a Visiting Ret. Professor at Banaras Hindu University, Varanasi, India. His research interests include lifetime analysis, ecological modeling, sampling theory, reliability analysis, statistical inference, and Bayesian inference.

Manoj Kumar Tiwari

Manoj Kumar Tiwari, Ph.D., is currently working as Associate Professor of Statistics at the Punjab University, Chandigarh, India, also he is a visiting professor at Sultan Qaboos University, AL-Khoud 123, Muscat, Oman. His area of research includes Life Time Experiments, Regression Analysis, Statistical Inference, and Bayesian inference. He has published a number of research articles in the national and international journals of repute. He has reviewed a number of research articles for several international journals.

Sandeep Kumar

Sandeep Kumar received his M.Phil. degree in statistics from Chaudhary Charan Singh University, Meerut, India, in 2019, and he has enrolled in Ph.D. (Statistics) from Central University of Haryana, India. His current research interests include ecological modeling and Bayesian inference.