A Bayesian shrinkage approach under symmetric and asymmetric loss functions for the Rayleigh distribution with the progressively type-II censoring schemes

Document Type : Original Scientific Paper

Authors

1 Department of Statistics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran

2 Department of Statistics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Abstract

The main goal of this paper is to achieve the Bayesian shrinkage estimators for the scale parameter of the Rayleigh distribution with progressively type-II censoring data‎. ‎The best linear estimators are also presented under the squared error and linear exponential loss functions‎. ‎Furthermore‎, ‎the relative efficiency of the proposed Bayesian shrinkage estimators is calculated for the best linear estimators‎. ‎Finally‎, ‎through a numerical analysis‎, ‎the relative efficiency of the Bayesian shrinkage estimators is compared with the best linear estimators.

Keywords

Main Subjects


Aggarwala, R. and Balakrishnan, N. (1998). Some properties of progressive censored order statistics from arbitrary and uniform distributions with applications to inference and simulation. Journal of Statistical Planning and Inference, 70(1):35–49.
Ahmadi, J., Doostparast, M. and Parsian, A. (2005). Estimation and prediction in a two-parameter Exponential distribution based on k-record values under LINEX loss function. Communications in Statistics–Theory and Methods, 34(4):795–805.
Asar, Y. and Arabi Belaghi, R. (2023). Estimation in Weibull distribution under progressively type-I hybrid censored data. REVSTAT-Statistical Journal, 20(5):563–586.
Balakrishnan, N. and Aggarwala, R. (2000). Progressive Censoring: Theory, Methods and Applications. Boston: Birkhäuser.
Balakrishnan, N., Cramer, E., Kamps, U. and Schenk, N. (2001). Progressive type-II censored order statistics from exponential distributions. Statistics, 35(4):537–556.
Balakrishnan, N. and Sandhu, R.A. (1995). A simple simulational algorithm for generating progressive type-II censored samples. The American Statistician, 49(2):229–230.
Balakrishnan, N. and Sandhu, R.A. (1996). Best linear unbiased and maximum likelihood estimation for exponential distribution under general progressive type-II censored samples. Sankhyā: The Indian Journal of Statistics, Series B:1–9.
Bandyopadhyay, U. and Chattopadhyay, G. (1995). Progressive censoring under inverse sampling for nonparametric two-sample problems. Sequential Analysis, 14(1):1–28.
Basiri, E. and Beigi, S. (2021). Bayesian two-sample prediction problem for the Rayleigh distribution under progressively type-II censoring with random removals. Caspian Journal of Mathematical Sciences, 10(2):156–175.
Dey, S., Dey, T. and Maiti, S.S. (2015). Bayes shrinkage estimation of the parameter of Rayleigh distribution for progressive type-II censored data. Austrian Journal of Statistics, 44(4):3–15.
Dey, T., Dey, S. and Kundu, D. (2016). On progressively type-II censored two-parameter Rayleigh distribution. Communications in Statistics-Simulation and Computation, 45(2):438–455.
Dey, S., Singh, S., Tripathi, Y.M. and Asgharzadeh, A. (2023). Estimation and prediction for a progressively censored generalized inverted exponential distribution. Statistical Methodology, 32:185–202.
Fernandez, A.J. (2004). On estimating exponential parameters with general type II progressive censoring. Journal of Statistical Planning and Inference, 121(1):135–147.
Guilbaud, O. (2001). Exact non-parametric confidence intervals for quantiles with progressive type-II censoring. Scandinavian Journal of Statistics, 28(4):699–713.
Jia, X., Nadarajah, S. and Guo, B. (2018). Exact inference on Weibull parameters with multiply Type-I censored data. IEEE Transactions on Reliability, 67(2):432–445.
Kumar, D., Nassar, M. and Dey, S. (2023). Progressive type-II censored data and associated inference with application based on Li–Li Rayleigh distribution. Annals of Data Science, 10(1):43–71.
Lehmann, E.L. and Casella, G. (1998). Theory of Point Estimation. 2nd Edition, New York: Springer.
Marrelec, G., Benali, H., Ciuciu, P., Pélégrini-Issac, M. and Poline, J.B. (2003). Robust Bayesian estimation of the hemodynamic response function in event-related BOLD fMRI using basic physiological information. Human Brain Mapping, 19(1):1–17.
Polovko, A.M. (1968). Fundamentals of Reliability Theory. San Diego: Academic Press.
Prakash, G. and Singh, D.C. (2008). Shrinkage estimation in exponential type-II censored data under LINEX loss. Journal of the Korean Statistical Society, 37:53–61.
Prakash, G. and Singh, D.C. (2009). A Bayesian shrinkage approach in Weibull type-II censored data using prior point information. REVSTAT-Statistical Journal, 7(2):171–187.
Ren, J. and Gui, W. (2021). Inference and optimal censoring scheme for progressively Type-II censored competing risks model for generalized Rayleigh distribution. Computational Statistics, 36(1):479–513.
Singh, D.C., Prakash, G. and Singh, P. (2007). Shrinkage testimators for the shape parameter of Pareto distribution using LINEX loss function. Communications in Statistics-Theory and Methods, 4(36):741–753.
Thompson, J.R. (1968). Some shrunken techniques for estimating the mean. Journal of the American Statistical Association, 63(321):113–122.
Tolba, A.H., Abushal, T.A. and Ramadan, D.A. (2023). Statistical inference with joint progressive censoring for two populations using power Rayleigh lifetime distribution. Scientific Reports, 13(1):3832.
Viveros, R. and Balakrishnan, N. (1994). Interval estimation of life characteristics from progressively censored samples. Technometrics, 36(1):84–91.
Yuen, H.K. and Tse, S.K. (1996). Parameters estimation for Weibull distributed lifetimes under progressive censoring with random removals. Journal of Statistical Computation and Simulation, 55(1-2):57–71.
Zellner, A. (1986). Bayesian estimation and prediction using asymmetric loss functions. Journal of the American Statistical Association, 81(394):446–451.