Bayesian Estimation of Exponentiated Inverse Rayleigh Distribution

Arun Kumar Rao; Himanshu Pandey

doi:10.18535/ijsrm/v9i03.m01

Abstract

In this paper, exponentiated inverse Rayleigh distribution is considered for Bayesian analysis. The expressions for Bayes estimators of the parameter have been derived under squared error, precautionary, entropy, K-loss, and Al-Bayyati’s loss functions by using quasi and gamma priors.

Keywords

Bayesian methodexponentiated inverse Rayleigh distributionquasi and gamma priorssquared errorprecautionaryentropyK-lossand Al-Bayyati’s loss functions

References

Rao, G.S. and Mbwambo, S., (2019): “Exponentiated inverse Rayleigh distribution and an application to coating weights of iron sheets data”. Journal of Probability and Statistics, Vol. 2019, Article ID 7519429, 13 pages.Google Scholar ↗
Zellner, A., (1986): “Bayesian estimation and prediction using asymmetric loss functions”. Jour. Amer. Stat. Assoc., 91, 446-451.Google Scholar ↗
Basu, A. P. and Ebrahimi, N., (1991): “Bayesian approach to life testing and reliability estimation using asymmetric loss function”. Jour. Stat. Plann. Infer., 29, 21-31.Google Scholar ↗
Norstrom, J. G., (1996): “The use of precautionary loss functions in Risk Analysis”. IEEE Trans. Reliab., 45(3), 400-403.Google Scholar ↗
Calabria, R., and Pulcini, G. (1994): “Point estimation under asymmetric loss functions for left truncated exponential samples”. Comm. Statist. Theory & Methods, 25 (3), 585-600.Google Scholar ↗
D.K. Dey, M. Ghosh and C. Srinivasan (1987): “Simultaneous estimation of parameters under entropy loss”. Jour. Statist. Plan. And infer., 347-363.Google Scholar ↗
D.K. Dey, and Pei-San Liao Liu (1992): “On comparison of estimators in a generalized life Model”. Microelectron. Reliab. 32 (1/2), 207-221.Google Scholar ↗
Wasan, M.T., (1970): “Parametric Estimation”. New York: Mcgraw-Hill.Google Scholar ↗
Al-Bayyati, (2002): “Comparing methods of estimating Weibull failure models using simulation”. Ph.D. Thesis, College of Administration and Economics, Baghdad University, Iraq.Google Scholar ↗

[refR-1] Rao, G.S. and Mbwambo, S., (2019): “Exponentiated inverse Rayleigh distribution and an application to coating weights of iron sheets data”. Journal of Probability and Statistics, Vol. 2019, Article ID 7519429, 13 pages.Google Scholar ↗

[refR-2] Zellner, A., (1986): “Bayesian estimation and prediction using asymmetric loss functions”. Jour. Amer. Stat. Assoc., 91, 446-451.Google Scholar ↗

[refR-3] Basu, A. P. and Ebrahimi, N., (1991): “Bayesian approach to life testing and reliability estimation using asymmetric loss function”. Jour. Stat. Plann. Infer., 29, 21-31.Google Scholar ↗

[refR-4] Norstrom, J. G., (1996): “The use of precautionary loss functions in Risk Analysis”. IEEE Trans. Reliab., 45(3), 400-403.Google Scholar ↗

[refR-5] Calabria, R., and Pulcini, G. (1994): “Point estimation under asymmetric loss functions for left truncated exponential samples”. Comm. Statist. Theory & Methods, 25 (3), 585-600.Google Scholar ↗

[refR-6] D.K. Dey, M. Ghosh and C. Srinivasan (1987): “Simultaneous estimation of parameters under entropy loss”. Jour. Statist. Plan. And infer., 347-363.Google Scholar ↗

[refR-7] D.K. Dey, and Pei-San Liao Liu (1992): “On comparison of estimators in a generalized life Model”. Microelectron. Reliab. 32 (1/2), 207-221.Google Scholar ↗

[refR-8] Wasan, M.T., (1970): “Parametric Estimation”. New York: Mcgraw-Hill.Google Scholar ↗

[refR-9] Al-Bayyati, (2002): “Comparing methods of estimating Weibull failure models using simulation”. Ph.D. Thesis, College of Administration and Economics, Baghdad University, Iraq.Google Scholar ↗