Advertisement

Burr–Hatke Exponential Distribution: A Decreasing Failure Rate Model, Statistical Inference and Applications

  • Abhimanyu Singh Yadav
  • Emrah AltunEmail author
  • Haitham M. Yousof
Article
  • 25 Downloads

Abstract

In this paper, we introduce a new one-parameter lifetime distribution as an alternative to exponential distribution named as Burr–Hatke exponential (BHE) distribution. Classical and Bayesian estimation procedure for the estimation of BHE model parameter are discussed using on the Type-II hybrid censored data. The Monte Carlo simulations are performed to compare the performances of the obtained estimators in mean square error sense. Two real data sets are analyzed for the illustrative purpose of the considered study. Additionally, a new log-location regression model based on the new distribution is introduced and studied.

Keywords

Exponential Burr–Hatke Hybrid censoring Bayesian estimation Approximation techniques Regression 

Notes

References

  1. 1.
    Asgharzadeh A, Valiollahi R, Kundu D (2013) Prediction for future failures in Weibull distribution under hybrid censoring. J Stat Comput Simul 85:824–838.  https://doi.org/10.1080/00949655.2013.848451 Google Scholar
  2. 2.
    Balakrishnan N, Kundu D (2013) Hybrid censoring: models, inferential results and applications. Comput Stat Data Anal 57(1):166–209Google Scholar
  3. 3.
    Cordeiro GM, de Castro M (2011) A new family of generalized distributions. J Stat Comput Simul 81(7):883–898Google Scholar
  4. 4.
    Chen S, Bhattacharya GK (1988) Exact confidence bounds for an exponential parameter under hybrid censoring. Commun Stat Theor Methods 17:1857–1870Google Scholar
  5. 5.
    Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible and HPD intervals. J Comput Graph Stat 8(1):69–92Google Scholar
  6. 6.
    Chhikara RS, Folks JL (1977) The inverse Gaussian distribution as a lifetime model. Technometrics 19(4):461–468Google Scholar
  7. 7.
    Childs A, Chandrasekar B, Balakrishnan N, Kundu D (2003) Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution. Ann Inst Stat Math 55(2):319–330Google Scholar
  8. 8.
    Efron B (1988) Logistic regression, survival analysis, and the Kaplan–Meier curve. J Am Stat Assoc 83(402):414–425Google Scholar
  9. 9.
    Epstein B (1954) Truncated life tests in the exponential case. Ann Math Stat 25:555–564Google Scholar
  10. 10.
    Gelfand AE, Smith AF (1990) Sampling-based approaches to calculating marginal densities. J Am Stat Assoc 85(410):398–409Google Scholar
  11. 11.
    Korkmaz MÇ, Yousof HM (2017) The one-parameter odd lindley exponential model: mathematical properties and applications. Stoch Qual Control 32(1):25–35Google Scholar
  12. 12.
    Lindley DV (1980) Approximate Bayesian methods. Trabajos de estadística y de investigación operativa 31(1):223–245Google Scholar
  13. 13.
    Merovci F (2013) Transmuted exponentiated exponential distribution. Math Sci Appl E-Notes 1(2):112–122Google Scholar
  14. 14.
    Nadarajah S, Kotz S (2006) The beta exponential distribution. Reliab Eng Syst Saf 91(6):689–697Google Scholar
  15. 15.
    Rasekhi M, Alizadeh M, Altun E, Hamedani GG, Afify AZ, Ahmad M (2017) The modified exponential distribution with applications. Pak J Stat 33(5):383–398Google Scholar
  16. 16.
    Singh R, Singh SK, Singh U, Singh GP (2008) Bayes estimator of generalized-exponential parameters under Linex loss function using Lindley’s approximation. Data Sci J 7:65–75Google Scholar
  17. 17.
    Singh U, Singh SK, Yadav AS (2015) Bayesian estimation for extension of exponential distribution under progressive Type-II censored data using Markov chain Monte Carlo method. J Stat Appl Probab 4(2):275Google Scholar
  18. 18.
    Singh SK, Singh U, Yadav AS (2014) Bayesian estimation of Marshall–Olkin extended exponential parameters under various approximation techniques. Hacet J Math Stat 43(2):347–360Google Scholar
  19. 19.
    Upadhyay SK, Vasishta N, Smith AFM (2001) Bayes inference in life testing and reliability via Markov chain Monte Carlo simulation. Sankhya Indian J Stat Ser A 63(1):15–40Google Scholar
  20. 20.
    Yadav AS, Singh SK, Singh U (2016) Bayes Estimator of the parameter and reliability function of Marshall–Olkin extended exponential distribution using hybrid Type-II censored data. J Stat Manag Syst 19(3):325–344.  https://doi.org/10.1080/09720510.2014.943091 Google Scholar
  21. 21.
    Yadav AS, Singh SK, Singh U (2016) On hybrid censored inverse Lomax distribution: application to the survival data. Statistica 76:185–203Google Scholar
  22. 22.
    Yadav AS, Yang M (2018) On Type-II hybrid censored two parameter Rayleigh distribution. Int J Math Comput 29(1):11–24Google Scholar
  23. 23.
    Yadav AS, Saha M, Singh SK, Singh U (2018) Bayesian estimation of the parameter and the reliability characteristics of xgamma distribution using Type-II hybrid censored. Life Cycle Reliab Saf Eng 8:1–10.  https://doi.org/10.1007/s41872-018-0065-5 Google Scholar
  24. 24.
    Yousof HM, Altun E, Ramires TG, Alizadeh M, Rasekhi M (2018) A new family of distributions with properties, regression models and applications. J Stat Manag Syst 21(1):163–188Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Abhimanyu Singh Yadav
    • 1
  • Emrah Altun
    • 2
    Email author
  • Haitham M. Yousof
    • 3
  1. 1.Department of StatisticsCentral University of RajasthanKishangarhIndia
  2. 2.Department of StatisticsBartin UniversityBartinTurkey
  3. 3.Department of Statistics, Mathematics and InsuranceBenha UniversityBenhaEgypt

Personalised recommendations