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Bayesian Reliability Analysis of Marshall and Olkin Model

  • Mohammed H. AbuJaradEmail author
  • Athar Ali Khan
  • Mundher A. Khaleel
  • Eman S. A. AbuJarad
  • Ali H. AbuJarad
  • Pelumi E. Oguntunde
Article
  • 26 Downloads

Abstract

In this paper, an endeavor has been made to fit three distributions Marshall–Olkin with exponential distributions, Marshall–Olkin with exponentiated exponential distributions and Marshall–Olkin with exponentiated extension distribution keeping in mind the end goal to actualize Bayesian techniques to examine visualization of prognosis of women with breast cancer and demonstrate through utilizing Stan. Stan is an abnormal model dialect for Bayesian displaying and deduction. This model applies to a genuine survival controlled information with the goal that every one of the ideas and calculations will be around similar information. Stan code has been created and enhanced to actualize a censored system all through utilizing Stan technique. Moreover, parallel simulation tools are also implemented and additionally actualized with a broad utilization of rstan.

Keywords

Marshall–Olkin with exponential Marshall–Olkin with exponentiated exponential Marshall–Olkin with exponentiated extension Posterior Simulation rstan Bayesian inference HMC 

Notes

References

  1. 1.
    AbuJarad MH, AbuJarad ESA, Khan AA (2019) Bayesian survival analysis of type I general exponential distributions. Ann Data Sci.  https://doi.org/10.1007/s40745-019-00228-1 CrossRefGoogle Scholar
  2. 2.
    AbuJarad MH, Khan AA (2018) Bayesian survival analysis of Topp–Leone generalized family with Stan. Int J Stat Appl 8(5):274–290Google Scholar
  3. 3.
    AbuJarad MH, Khan AA (2018) Exponential model: a Bayesian study with Stan. Int J Recent Sci Res 9(8):28495–28506Google Scholar
  4. 4.
    Akhtar MT, Khan AA (2014) Bayesian analysis of generalized log-Burr family with R. SpringerPlus 3(1):185CrossRefGoogle Scholar
  5. 5.
    Carlin BP, Louis TA (2008) Bayesian methods for data analysis. CRC Press, Boca RatonGoogle Scholar
  6. 6.
    Carpenter B, Gelman A, Hoffman MD, Lee D, Goodrich B, Betancourt M, Brubaker M, Guo J, Li P, Riddell A (2017) Stan: a probabilistic programming language. J Stat Softw 76(1):1–32CrossRefGoogle Scholar
  7. 7.
    Collet D (1994) Modelling survival data in medical research. Chapman & Hall, LondonCrossRefGoogle Scholar
  8. 8.
    Evans M, Swartz T et al (1995) Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems. Stat Sci 10(3):254–272CrossRefGoogle Scholar
  9. 9.
    Gelman A et al (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1(3):515–534CrossRefGoogle Scholar
  10. 10.
    Gelman A, Rubin DB et al (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472CrossRefGoogle Scholar
  11. 11.
    Gelman A, Stern HS, Carlin JB, Dunson DB, Vehtari A, Rubin DB (2014) Bayesian data analysis. Chapman and Hall/CRC, LondonGoogle Scholar
  12. 12.
    Gupta RD, Kundu D (1999) Theory & methods: generalized exponential distributions. Aust N Z J Stat 41(2):173–188CrossRefGoogle Scholar
  13. 13.
    Hoffman MD, Gelman A (2014) The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res 15(1):1593–1623Google Scholar
  14. 14.
    Leathem AJ, SusanA Brooks (1987) Predictive value of lectin binding on breast-cancer recurrence and survival. Lancet 329(8541):1054–1056CrossRefGoogle Scholar
  15. 15.
    Marshall AW, Olkin I (1997) A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika 84(3):641–652CrossRefGoogle Scholar
  16. 16.
    Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 57(1):1087–1092CrossRefGoogle Scholar
  17. 17.
    Neal RM et al (2011) MCMC using Hamiltonian dynamics. In: Handbook of Markov chain Monte Carlo, vol 11, p 2 Google Scholar
  18. 18.
    Oguntunde PE, Khaleel MA, Okagbue HI, Odetunmibi OA (2019) The Topp–Leone Lomax (TLLo) distribution with applications to airbone communication transceiver dataset. Wirel Pers Commun 109:349–360CrossRefGoogle Scholar
  19. 19.
    Singh GN, Khalid M (2015) Exponential chain dual to ratio and regression type estimators of population mean in two-phase sampling. Statistica 75(4):379–389Google Scholar
  20. 20.
    Stan Development Team (2017) Stan: a C++ library for probability and sampling. Version 2.14.0Google Scholar
  21. 21.
    Stan Development Team et al (2016) Stan modeling language: user’s guide and reference manual. VersionGoogle Scholar
  22. 22.
    Tierney L, Kass RE, Kadane JB (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J Am Stat Assoc 84(407):710–716CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Statistics and Operations ResearchAMUAligarhIndia
  2. 2.Department of MathematicsAMUAligarhIndia
  3. 3.Gaza UniversityGazaPalestine
  4. 4.Department of Mathematics, Faculty of Computer Science and MathematicsUniversity of TikritTikrītIraq
  5. 5.Department of MathematicsCovenant UniversityOtaNigeria

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