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Classical and Bayes estimation of reliability characteristics of the Kumaraswamy-Inverse Exponential distribution

  • M. K. Rastogi
  • P. E. OguntundeEmail author
Original Article
  • 57 Downloads

Abstract

In this research, the Bayesian estimators of both the unknown model parameters, survivor (or reliability) function and failure rate of the three-parameter Kumaraswamy-Inverse Exponential distribution were obtained. The symmetric and asymmetric loss functions were used for the Bayesian estimations. Though, the Bayes estimators could not be obtained in explicit forms. Random samples were generated from the posterior distributions using the Metropolis Hastings algorithm procedure and the Bayes estimators were obtained. Comparison was made between the Bayes estimators and the maximum likelihood estimators using Monte Carlo simulations. In addition, the Bayes estimators of the reliability characteristics were all obtained whilst making use of both the symmetric and asymmetric loss functions. However, their performance was compared through their simulated risks. Furthermore, a numerical study was conducted in order to compare the proposed estimates using simulations while illustrative examples were also presented. Two real life data sets were analyzed for the case when all the three parameters are unknown.

Keywords

Bayesian inference Kumaraswamy Inverse Exponential distribution Mathematical statistics Maximum likelihood estimation MH algorithm Reliability analysis Simulation 

References

  1. Abouammoh AM, Alshingiti AM (2009) Reliability of generalized inverted exponential distribution. J Stat Comput Simul 79:1301–1315MathSciNetCrossRefzbMATHGoogle Scholar
  2. Cordeiro GM, de Castro M (2011) A New family of generalized distributions. J Stat Comput Simul 81:883–898MathSciNetCrossRefzbMATHGoogle Scholar
  3. de Gusmao FRS, Tomazella VLD, Ehlers RS (2017) Bayesian estimation of the Kumaraswamy inverse Weibull distribution. J Stat Theory Appl 16:248–260MathSciNetGoogle Scholar
  4. Hastings WK (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57:97–109MathSciNetCrossRefzbMATHGoogle Scholar
  5. Keller AZ, Kamath AR (1982) Reliability analysis of CNC machine tools. Reliab Eng 3:449–473CrossRefGoogle Scholar
  6. Mead ME, Abd-Eltawab AR (2014) A note on Kumaraswamy Frchet distribution. Aust J Basic Appl Sci 8:294–300Google Scholar
  7. Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equations of state calculations by fast computing machines. J Chem Phys 21:1087–1092CrossRefGoogle Scholar
  8. Nichols MD, Padgett WJ (2006) A bootstrap control chart for Weibull percentiles. Qual Reliab Eng Int 22:141–151CrossRefGoogle Scholar
  9. Oguntunde PE, Babatunde OS, Ogunmola AO (2014) Theoretical analysis of the Kumaraswamy-inverse exponential distribution. Int J Stat Appl 4:113–116Google Scholar
  10. Oguntunde PE, Adejumo AO, Owoloko EA (2017a) The Weibull-inverted exponential distribution: a generalization of the inverse exponential distribution. Lecture Notes in Engineering and Computer Science. In: Proceedings of the world congress on engineering, 5–7 July, London, UK, pp 16–19Google Scholar
  11. Oguntunde PE, Adejumo AO, Owoloko EA (2017b) On the exponentiated generalized inverse exponential distribution. Lecture Notes in Engineering and Computer Science. In: Proceedings of the world congress on engineering, 5–7 July, London, UK, pp 80–83Google Scholar
  12. Oguntunde PE, Adejumo AO, Owoloko EA (2017c) Application of Kumaraswamy inverse exponential distribution to real lifetime data. Int J Appl Math Stat 56:34–47MathSciNetGoogle Scholar
  13. Rastogi MK, Merovci F (2017) Bayesian estimation for parameters and reliability characteristic of the Weibull Rayleigh distribution. J King Saud Univ Sci.  https://doi.org/10.1016/j.jksus.2017.05.008 Google Scholar
  14. Singh B, Goel R (2015) The beta inverted exponential distribution: properties and applications. Int J Appl Sci Math 2:132–141Google Scholar
  15. Smith RL, Naylor JC (1987) A comparison of maximum likelihood and Bayesian estimators for the three-parameter Weibull distribution. Appl Stat 36:358–369MathSciNetCrossRefGoogle Scholar
  16. Varian HR (1975) A Bayesian approach to real estate assessment. In: Fienberg SE, Zellner A (eds) Studies in Bayesian econometrics and statistics. North Holland, Amsterdam, pp 195–208Google Scholar
  17. Zellner A (1986) Bayesian estimation and prediction using asymetric loss function. J Am Stat Assoc 81:446–451CrossRefzbMATHGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2018

Authors and Affiliations

  1. 1.National Institute of Pharmaceutical Education and ResearchHajipurIndia
  2. 2.Department of MathematicsCovenant UniversityOtaNigeria

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