Some results on Bayes estimation under Linex loss function

Document Type : Research Paper

Authors

1 Faculty of Mathematical Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

2 Department of Statistics, University of University of Mohaghegh Ardabili, P.O.Box 56199-11367, Ardabili, Iran

Abstract

In this paper, we introduced straightforward formulas for the Bayes risk linked to the Linex loss function, which we then applied to estimate parameters of the normal, Poisson, and fractional Weibull distributions.
We aimed to investigate the development of a linear Bayes estimator using the Linex loss function and successfully derived it for the normal and Poisson scenarios.
We also demonstrated the process of creating empirical Bayes estimates using Linex loss and applied it to observed frequencies fn(x)$
produced by the Poisson-gamma model.

Keywords

References

[1] A. K. Gupta and D. K. Nagar, Matrix Variate Distributions, Wiley-VCH, CRC. (2000).
[2] A. P. Basu and N. Ebrahimi, Bayesian approach to life testing and reliability estimation using asymmetric loss function, Journal of Statistical Planning and Inference. 29 (1991) 21-31.
[3] A. Parsian and N. Parsipour On the admissibility and inadmissibility of estimators of scale parameter using an asymmetric loss function, Communications in Statistics - Theory and Methods. 22(1993) 2877-2901.
[4] A. Zellner, Bayesian estimation and prediction using asymmetric loss function, Journal of the American Statistical Association. 81 (1986) 446-451.
[5] A. Zellner and M. S. Giesel, Sensitivity of control to uncertainty and from of the criterion function. In Future of Statistics D. G. Watts (ed.), Academic Press, New York. (1968) 269-289.
[6] C. A. Gnecco, Bayesian decision theoretic phase-II clinical trial designs using asymmetric loss, In Bayesian Analysis in Statistics and Econometric: Berry D. A. et. al. (eds), John Wiley and sons Inc. (1996) 483-492.
[7] F. A. Spiring, The re ected normal loss function, Canadian Journal of Statistics. 21(3) (1993) 321-330.
[8] H. R. Varian, A Bayesian approach to real estate assessment. In Studies in Bayesian Econometrics and Statistics S. E. Fienberg and A. Zellner (eds.), North - Holland Amsterdam. (1975) 195-208.
[9] H. Schabe, Bayes estimates under asymmetric loss, IEEE transactions on reliability. 40 (1992) 63-67.
[10] H. V. Roberts, Reporting of Bayesian studies, In Studies in Bayesian Econometrics and Statistics S. E. Fienbrrg and A. Zellner (eds.), North-Holland, New York. (1975) 465-483.
[11] J. S. Maritz and T. Lwin, Empirical Bayes Methods, Chapman & Hall, New York, II-Edition. (1989).
[12] M. Ganji and F. Gharari, Bayesian estimation in delta and nabla discrete fractional Weibull distributions, Journal of Probability and Statistics. 8 (2016) Article ID 1969701.
[13] R. D. Thompson and A. P. Basu, Asymmetric loss function for estimating system reliability. (In Bayesian Analysis in Statistics and Econometric: Berry, D. A. et. al. (eds.), John Wiley and sons. (1996).
[14] S. M. Sadooghi-Alvandi, Estimation of the parameter of a Poisson distribution using a Linex loss function, Australian & New Zealand Journal of Statistics. 32(2)(1990) 393-398.
[15] Y. C. Chang and W. L. Hung, Linex Loss Functions with Applications to Determining the Optimum Process Parameters, Quality & Quantity. 41 (2007) 291-301.
DOI 10.1007/s11135-005-5425-3.
[16] J.S. Maritz and T. Lwin, Empirical Bayes Methods (1st ed.). Routledge. (1989)
https://doi.org/10.4324/9781351140645.
Journal of Hyperstructures
Volume 13, Issue 1
2024
Pages 79-93

Files

Share

How to cite

Statistics