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E-Bayesian and Hierarchical Bayesian Estimation for the Shape Parameter and Reversed Hazard Rate of Power Function Distribution Under Different Loss Functions

  • E. I. Abdul-SatharEmail author
  • R. B. Athira Krishnan
Research article
  • 40 Downloads

Abstract

This paper presents the E-Bayesian and hierarchical Bayesian estimation of the shape parameter and reversed hazard rate of Power function distribution under the condition that scale parameter is known, based on the different loss functions. We also study some important properties of the proposed estimators. Based on Monte Carlo Simulation study and using a real dataset comparisons are made between the proposed estimators and existing Bayesian estimators. Confidence intervals and coverage probability of the estimators are also computed. From the numerical studies it can be seen that the proposed E-Bayesian and hierarchical Bayesian estimators have better performance when compared to the existing Bayesian estimators in terms of bias and MSE respectively.

Keywords

E-Bayesian estimation Hierarchical Bayesian estimation Loss function Prior/posterior distribution Reversed hazard rate Credible interval and coverage probability 

Notes

Acknowledgements

The authors would like to thank the Editor in Chief and the reviewers for their constructive comments which helped to improve the quality of the present paper to a great extend.

References

  1. Abdul-Sathar E, Renjini K, Rajesh G, Jeevanand E (2015) Bayes estimation of lorenz curve and gini-index for power function distribution. S Afr Stat J 49(1):21–33MathSciNetzbMATHGoogle Scholar
  2. Ali MM, Woo J, Nadarajah S (2005) On the ratic x/(x+ y) for the power function distribution. Pak J Stat All Ser 21(2):131zbMATHGoogle Scholar
  3. Ando T, Zellner A et al (2010) Hierarchical bayesian analysis of the seemingly unrelated regression and simultaneous equations models using a combination of direct monte carlo and importance sampling techniques. Bayesian Anal 5(1):65–95MathSciNetCrossRefGoogle Scholar
  4. Arslan G (2014) A new characterization of the power distribution. J Comput Appl Math 260:99–102MathSciNetCrossRefGoogle Scholar
  5. Bagchi S, Sarkar P (1986) Bayes interval estimation for the shape parameter of the power distribution. IEEE Trans Reliab 35(4):396–398CrossRefGoogle Scholar
  6. Belzunce F, Candel J, Ruiz J (1998) Ordering and asymptotic properties of residual income distributions. Sankhyā Indian J Stat Ser B 60:331–348MathSciNetzbMATHGoogle Scholar
  7. Berger JO (1985) Statistical decision theory and Bayesian analysis. Springer, BerlinCrossRefGoogle Scholar
  8. Childs A, Balakrishnan N (2002) Conditional inference procedures for the pareto and power function distributions based on type-II right censored samples. Statistics 36(3):247–257MathSciNetCrossRefGoogle Scholar
  9. Han M (1997) The structure of hierarchical prior distribution and its applications. Chin Oper Res Manag Sci 6(3):31–40MathSciNetGoogle Scholar
  10. Han M (2009) E-Bayesian estimation and hierarchical bayesian estimation of failure rate. Appl Math Model 33(4):1915–1922MathSciNetCrossRefGoogle Scholar
  11. Han M (2011) E-Bayesian estimation of the reliability derived from binomial distribution. Appl Math Model 35(5):2419–2424MathSciNetCrossRefGoogle Scholar
  12. Han M (2017) The E-Bayesian and hierarchical Bayesian estimations of pareto distribution parameter under different loss functions. J Stat Comput Simul 87(3):577–593MathSciNetCrossRefGoogle Scholar
  13. Han M, Ding Y (2004) Synthesized expected Bayesian method of parametric estimate. J Syst Sci Syst Eng 13(1):98–111CrossRefGoogle Scholar
  14. Huss M, Holme P (2007) Currency and commodity metabolites: their identification and relation to the modularity of metabolic networks. IET Syst Biol 1(5):280–285CrossRefGoogle Scholar
  15. Jaheen ZF, Okasha HM (2011) E-Bayesian estimation for the burr type XII model based on type-2 censoring. Appl Math Model 35(10):4730–4737MathSciNetCrossRefGoogle Scholar
  16. Khan M, Islam H (2007) On stress and strength having power function distributions. Pak J Stat All Ser 23(1):83MathSciNetzbMATHGoogle Scholar
  17. Lindley DV, Smith AF (1972) Bayes estimates for the linear model. J R Stat Soc Ser B (Methodol) 34:1–41MathSciNetzbMATHGoogle Scholar
  18. Lutful Kabir A, Ahsanullah M (1974) Estimation of the location and scale parameters of a power-function distribution by linear functions of order statistics. Commun Stat Theory Methods 3(5):463–467MathSciNetzbMATHGoogle Scholar
  19. Meniconi M, Barry D (1996) The power function distribution: a useful and simple distribution to assess electrical component reliability. Microelectron Reliab 36(9):1207–1212CrossRefGoogle Scholar
  20. Osei FB, Duker AA, Stein A (2011) Hierarchical Bayesian modeling of the space–time diffusion patterns of cholera epidemic in Kumasi, Ghana. Stat Neerl 65(1):84–100MathSciNetCrossRefGoogle Scholar
  21. Rahman H, Roy M, Baizid AR (2012) Bayes estimation under conjugate prior for the case of power function distribution. Am J Math Stat 2(3):44–48CrossRefGoogle Scholar
  22. Saleem M, Aslam M, Economou P (2010) On the Bayesian analysis of the mixture of power function distribution using the complete and the censored sample. J Appl Stat 37(1):25–40MathSciNetCrossRefGoogle Scholar
  23. Tavangar M (2011) Power function distribution characterized by dual generalized order statistics. J Iran Stat Soc 10(1):13–27MathSciNetzbMATHGoogle Scholar
  24. Zaka A, Akhter AS (2014) Bayesian analysis of power function distribution using different loss functions. Int J Hybrid Inf Technol 7(6):229–244CrossRefGoogle Scholar
  25. Zarrin S, Saxena S, Kamal M (2013) Reliability computation and bayesian analysis of system reliability of power function distribution. Int J Adv Eng Sci Technol 2(4):76–86Google Scholar

Copyright information

© The Indian Society for Probability and Statistics (ISPS) 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of KeralaThiruvananthapuramIndia

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