Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Bayes and Empirical Bayes Estimation of the Scale Parameter of the Gamma Distribution under Balanced Loss Functions

  • Rezaeian, R. (Department of Mathematics, Noor Islamic Azad University) ;
  • Asgharzadeh, A. (Department of Statistics, Faculty of Basic Science, University of Mazandaran)
  • Published : 2007.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

The present paper investigates estimation of a scale parameter of a gamma distribution using a loss function that reflects both goodness of fit and precision of estimation. The Bayes and empirical Bayes estimators rotative to balanced loss functions (BLFs) are derived and optimality of some estimators are studied.

Keywords

References

  1. Chung, Y., Kim, C. and Song, S. (1998). Linear estimators of a Poisson mean under balanced loss functions. Statistics & Decisions, 16, 245-257
  2. Dey, D. K., Ghosh, M. and Strawderman, W. E. (1999). On estimation with balanced loss functions. Statistics & Probability Letters, 45, 97-101 https://doi.org/10.1016/S0167-7152(99)00047-4
  3. Gruber, M. H. J. (2004). The efficiency of shrinkage estimators with respect to Zellner's balanced loss function. Communications in Statistics- Theory and Methods, 33, 235-249 https://doi.org/10.1081/STA-120028372
  4. Martiz, J. L. and Lwin, T. (1989). Empirical Bayes Methods. 2nd ed, Chapman Hall, London
  5. Rodrigues, J. and Zellner, A. (1995). Weighted balanced loss function for the exponential mean time to failure. Communications in Statistics-Theory and Methods, 23, 3609-3616 https://doi.org/10.1080/03610929408831468
  6. Sanjari Farsipour, N. and Asgharzadeh, A. (2004). Estimation of a normal mean relative to balanced loss functions. Statistical Papers, 45, 279-286 https://doi.org/10.1007/BF02777228
  7. Sanjari Farsipour, N. and Asgharzadeh, A. (2003). Bayesian multivariate normal analysis under balanced loss function. Pakistan Journal of Statistics, 19, 231-240
  8. Zellner, A. (1994). Bayesian and Non-Bayesian estimation using balanced loss functions. Statistical Decision Theorν and Related Topics V, (J. O. Berger and S. S. Gupta, eds), 377-390, Springer-Verlag, New York

Cited by

  1. Two-sided empirical Bayes test for location parameter in the gamma distribution vol.46, pp.9, 2017, https://doi.org/10.1080/03610926.2015.1080842