Journal of the Iranian Statistical Society

Performance of a Class of Bayes Shrinkage Estimators Based on Rayleigh Record Data under Reflected Gamma Loss Function

Authors

1 Department of Statistics, University of Mazandaran, Babolsar, Iran.

2 Department of Statistics, St. Anthony's College, Shillong, Meghalaya, India.

10.29252/jirss.18.2.155

Abstract

This article addresses the problem of Bayesian shrinkage estimation for the Rayleigh scale parameter based on record values under the reflected gamma loss (RGL) function. A class of Bayesian shrinkage estimators using prior point information is constructed. The risk functions of the maximum likelihood estimator (MLE) and proposed Bayesian shrinkage estimator are derived under the RGL function. The performance of Bayesian shrinkage estimator is compared with the MLE numerically and graphically. One data set has been analyzed to illustrate the performance of the Bayesian shrinkage estimator.

Keywords

Arnold, B.C., Balakrishnan, N., and Nagaraja, H.N. (1998). Records, John Wiley & Sons, New York. Baklizi, A., Asgharzadeh, A., and Shari¯, M. (2016). Estimation procedures based on preliminary test in exponential distribution under progressive censoring. Journal of Applied Statistical Science. 22, 141-152 Belaghi, A. R., Arashi, M., and Tabatabaey, S. M. M. (2015). On the construction of preliminary test estimator based on record values for the Burr XII model.Communications in Statistics-Theory and Methods, 44:1-23. Dey, Sanku and M.K. Das, M.K. (2007). A note on prediction interval for a Rayleigh distribution: Bayesian approach, Am. J. Math. Manage. Sci., 27 (12) 4348. Dey, Sanku (2009). Comparison of Bayes Estimators of the parameter and reliability function for Rayleigh distribution under di®erent loss functions, Malays. J. Math.Sci., 3, 247264. Dey, Sanku and Dey, Tanujit (2014). Statistical Inference for the Rayleigh distribution under progressively Type-II censoring with binomial removal. Applied Mathematical Modelling, 38, 974982. Dey, Sanku., Dey, T. and Maiti, S. (2015). Bayes shrinkage estimation of the parameter of Rayleigh distribution for progressive type-II censored data. Austrian Journalof Statistics, 44, 3-15. Dey, Sanku, Salehi, M and Ahmadi, Jafar (2017) Rayleigh distribution revisited via ranked set sampling. Metron, 75(1), 6985. Casella, G., Berger, R. (2001). Statistical Inference. 2nd Ed., Brooks/Cole. Lawless, J.F. (2003). Statistical models and methods for lifetime data. Wiley, New York. Kiapour, A. (2017). Bayes shrinkage estimator for the scale parameter of exponential distribution based on censored data. Journal of Statistical Sciences, 11, 119-131. Kiapour, A., and Naghizadeh Qomi (2016). Shrinkage preliminary test estimation under a precautionary loss function with applications on records and censored data, Journal of the Iranian Statistical Society, 15(2), 73-85. Meghnatisi, M., Nematollahi, N. (2009). Inadmissibility of usual and mixed estimators of two ordered gamma scale parameters under re°ected gamma loss function, Journal of Mathematical Extension, 3, 89-99. Naghizadeh Qomi (2017a). Improved estimation in Rayleigh type-II censored data under a bounded loss utilizing a point guess value. Journal of the Iranian Statistical Society, 16, 51-66. Naghizadeh Qomi (2017b). Bayesian shrinkage estimation based on Rayleigh type-II censored data, Communications in Statistics -Theory and Methods, 46, 9859-9868. Naghizadeh Qomi, M., Barmoodeh, L. (2015). Shrinkage testimation in exponential distribution based on records under asymmetric squared log error loss. Journal of Statistical Research of Iran. 12, 225-238. Naghizadeh Qomi, M., Nematollahi, N., Parsian, A. (2015). On admissibility and inadmissibility of estimators after selection under re°ected gamma loss function, Hacettepe Journal of Mathematics and Statistics. 5, 1109-1124. Polovko, A. M. (1968). Fundamentals of Reliability Theory. Academic Press, SanDiego. Prakash, G., Singh, D. C. (2008). Shrinkage estimation in exponential type-II censored data under LINEX loss. Journal of the Korean Statistical Society. 37, 53-61. Towhidi, M. and Behboodian, J. (1999). Estimation of a scale parameter under a reflected gamma loss functions, Iranian Journal of Science, 10, 256-269. Towhidi, M. and Behboodian, J. (2002). Minimax estimation of a bounded parameter under some bounded loss functions, Far East Journal of Theoretical Statistics. 6,39-48. Thompson, J. R. (1968). Some shrunken techniques for estimating the Mean. Journal of the American Statistical Association. 63, 113-122.
Journal of the Iranian Statistical Society
Volume 18, Issue 2
December 2019
Pages 155-172
  • Receive Date: 23 July 2022
  • Revise Date: 13 May 2024
  • Accept Date: 23 July 2022