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Erschienen in: Annals of Data Science 3/2020

22.11.2019

Bayesian Reliability Analysis of Marshall and Olkin Model

verfasst von: Mohammed H. AbuJarad, Athar Ali Khan, Mundher A. Khaleel, Eman S. A. AbuJarad, Ali H. AbuJarad, Pelumi E. Oguntunde

Erschienen in: Annals of Data Science | Ausgabe 3/2020

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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.

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Literatur
2.
Zurück zum Zitat AbuJarad MH, Khan AA (2018) Bayesian survival analysis of Topp–Leone generalized family with Stan. Int J Stat Appl 8(5):274–290 AbuJarad MH, Khan AA (2018) Bayesian survival analysis of Topp–Leone generalized family with Stan. Int J Stat Appl 8(5):274–290
3.
Zurück zum Zitat AbuJarad MH, Khan AA (2018) Exponential model: a Bayesian study with Stan. Int J Recent Sci Res 9(8):28495–28506 AbuJarad MH, Khan AA (2018) Exponential model: a Bayesian study with Stan. Int J Recent Sci Res 9(8):28495–28506
4.
Zurück zum Zitat Akhtar MT, Khan AA (2014) Bayesian analysis of generalized log-Burr family with R. SpringerPlus 3(1):185 CrossRef Akhtar MT, Khan AA (2014) Bayesian analysis of generalized log-Burr family with R. SpringerPlus 3(1):185 CrossRef
5.
Zurück zum Zitat Carlin BP, Louis TA (2008) Bayesian methods for data analysis. CRC Press, Boca Raton CrossRef Carlin BP, Louis TA (2008) Bayesian methods for data analysis. CRC Press, Boca Raton CrossRef
6.
Zurück zum Zitat 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):1–32 CrossRef 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):1–32 CrossRef
7.
Zurück zum Zitat Collet D (1994) Modelling survival data in medical research. Chapman & Hall, London CrossRef Collet D (1994) Modelling survival data in medical research. Chapman & Hall, London CrossRef
8.
Zurück zum Zitat Evans M, Swartz T et al (1995) Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems. Stat Sci 10(3):254–272 CrossRef Evans M, Swartz T et al (1995) Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems. Stat Sci 10(3):254–272 CrossRef
9.
Zurück zum Zitat Gelman A et al (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1(3):515–534 CrossRef Gelman A et al (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal 1(3):515–534 CrossRef
10.
Zurück zum Zitat Gelman A, Rubin DB et al (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472 CrossRef Gelman A, Rubin DB et al (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7(4):457–472 CrossRef
11.
Zurück zum Zitat Gelman A, Stern HS, Carlin JB, Dunson DB, Vehtari A, Rubin DB (2014) Bayesian data analysis. Chapman and Hall/CRC, London Gelman A, Stern HS, Carlin JB, Dunson DB, Vehtari A, Rubin DB (2014) Bayesian data analysis. Chapman and Hall/CRC, London
12.
Zurück zum Zitat Gupta RD, Kundu D (1999) Theory & methods: generalized exponential distributions. Aust N Z J Stat 41(2):173–188 CrossRef Gupta RD, Kundu D (1999) Theory & methods: generalized exponential distributions. Aust N Z J Stat 41(2):173–188 CrossRef
13.
Zurück zum Zitat Hoffman MD, Gelman A (2014) The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res 15(1):1593–1623 Hoffman MD, Gelman A (2014) The no-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res 15(1):1593–1623
14.
Zurück zum Zitat Leathem AJ, SusanA Brooks (1987) Predictive value of lectin binding on breast-cancer recurrence and survival. Lancet 329(8541):1054–1056 CrossRef Leathem AJ, SusanA Brooks (1987) Predictive value of lectin binding on breast-cancer recurrence and survival. Lancet 329(8541):1054–1056 CrossRef
15.
Zurück zum Zitat 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):641–652 CrossRef 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):641–652 CrossRef
16.
Zurück zum Zitat Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 57(1):1087–1092 CrossRef Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 57(1):1087–1092 CrossRef
17.
Zurück zum Zitat Neal RM et al (2011) MCMC using Hamiltonian dynamics. In: Handbook of Markov chain Monte Carlo, vol 11, p 2 Neal RM et al (2011) MCMC using Hamiltonian dynamics. In: Handbook of Markov chain Monte Carlo, vol 11, p 2
18.
Zurück zum Zitat 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 109:349–360 CrossRef 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 109:349–360 CrossRef
19.
Zurück zum Zitat Singh GN, Khalid M (2015) Exponential chain dual to ratio and regression type estimators of population mean in two-phase sampling. Statistica 75(4):379–389 Singh GN, Khalid M (2015) Exponential chain dual to ratio and regression type estimators of population mean in two-phase sampling. Statistica 75(4):379–389
20.
Zurück zum Zitat Stan Development Team (2017) Stan: a C++ library for probability and sampling. Version 2.14.0 Stan Development Team (2017) Stan: a C++ library for probability and sampling. Version 2.14.0
21.
Zurück zum Zitat Stan Development Team et al (2016) Stan modeling language: user’s guide and reference manual. Version Stan Development Team et al (2016) Stan modeling language: user’s guide and reference manual. Version
22.
Zurück zum Zitat Tierney L, Kass RE, Kadane JB (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J Am Stat Assoc 84(407):710–716 CrossRef Tierney L, Kass RE, Kadane JB (1989) Fully exponential Laplace approximations to expectations and variances of nonpositive functions. J Am Stat Assoc 84(407):710–716 CrossRef
Metadaten
Titel
Bayesian Reliability Analysis of Marshall and Olkin Model
verfasst von
Mohammed H. AbuJarad
Athar Ali Khan
Mundher A. Khaleel
Eman S. A. AbuJarad
Ali H. AbuJarad
Pelumi E. Oguntunde
Publikationsdatum
22.11.2019
Verlag
Springer Berlin Heidelberg
Erschienen in
Annals of Data Science / Ausgabe 3/2020
Print ISSN: 2198-5804
Elektronische ISSN: 2198-5812
DOI
https://doi.org/10.1007/s40745-019-00234-3

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