Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

Huda A. Rasheed


In the current study, we have been derived some Basyian estimators for the parameter and relia-bility function of the inverse Rayleigh distribution under Generalized squared error loss function. In order to get the best understanding of the behavior of Bayesian analysis, we consider non-informative prior for the scale parameter using Jefferys prior Information as well as informative prior density represented by Gamma distribution. Monte-Carlo simulation have been employed to compare the behavior of different estimates for the scale parameter and reliability function of in-verse Rayleigh distribution based on mean squared errors and Integrated mean squared errors, respectively. In the current study, we observed that more occurrence of Bayesian estimate using Generalized squared error loss function using Gamma prior is better than other estimates for all cases


Inverse Rayleigh distribution, Bayesian estimator, Generalized Squared error loss Function, Jefferys prior and Gamma prior

Full Text:



Gharraph, M. K., 1993. "Comparison of estimators of location measures of an in-verse Rayleigh distribution", The Egyp-tian statistical Journal, 37(2): 295-309.

Soliman, A., A. E. Amin and A. A. Aziz, 2010. "Estimation and prediction from inverse Rayleigh distribution based on lower record values", Applied Mathemat-ical Sciences, 4(62): 3057-3066.

Khan, M. SH.2014. "Modified Inverse Rayleigh Distribution", International

Journal of Computer Applications, 87(13): 0975-8887.

Dey, S., 2012. "Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution", Malay-sian Journal of Mathematical Sciences, 6(1): 113-124.

Sindhu, T. N., M. Aslam, N. Feroze, 2013. "Bayes estimation of the parame-ters of the inverse Rayleigh distribution for left censored data". ProbStat Forum, 6: 42-59.

Prakash, G., 2013. "Bayes estimation in the Inverse Rayleigh model", Electronic Journal of Applied Statistical Analysis, 6(1): 67-83.

Fan, G., 2015. "_ Bayes Estimation for Inverse Rayleigh Model under Different Loss Functions", Research Journal of Applied Sciences, Engineering and Technology 9(12): 1115-1118, 2015 ISSN: 2040-7459; e-ISSN: 2040-7467.

Rasheed, H. A., Ismail, S. Z. and Jabir, A. G.2015. "A Comparison of the Classi-cal Estimators with the Bayes Estimators of One Parameter Inverse Rayleigh Dis-tribution", International Journal of Ad-vanced.

Rasheed, H. A. and Aref, R. kh.2016. "Bayesian Approach in Estimation of Scale Parameter of Inverse Rayleigh dis-tribution", Mathematics and Statistics Journal, ISSN-2077-459, 2(1): 8-13.

Rasheed, H. A. and Aref, R. kh.2016. "Reliability Estimation in Inverse Ray-leigh Distribution using Precautionary Loss Function", Mathematics and Statis-tics Journal, ISSN-2077-4591, 2(3): 9-15.

Shawky, A. I. and M. M. Badr, 2012. "Estimations and prediction from the in-verse Rayleigh model based on lower record statistics", Life Science Journal, 9(2): 985-990.

Oliwi N. A., 2015, "Some Estimators of the Pareto Type I Distribution / A Com-parison Study ", M. Sc. Thesis in Math-

ematics, College of Science, Al-Mustansiriyah University.

Rasheed, H. A. and Al-Gazi, N. A., 2014. "Bayesian Estimation for the Reliability Function of Pareto Type I Distribution under Generalized Square Error Loss Function", International Journal of Engi-neering and Innovative Technology, 4(6): 33-40.

Rasheed, H. A. and R. kh. Aref, 2016. "Reliability Estimation in Inverse Ray-leigh Distribution using Precautionary Loss Function", Mathematics and Statis-tics Journal, ISSN-2077-4591, 2(3): 9-15.



  • There are currently no refbacks.

Copyright (c) 2018 Al-Mustansiriyah Journal of Science

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Copyright (c) 2018 by Al-Mustansiriyah Journal of Science
ISSN: 1814-635X (Print), ISSN: 2521-3520 (online)