The Bayesian Reliability Analysis of the Alpha Power Gompertz Model

Authors

  • Joseph Thomas Eghwerido Department of Statistics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria
  • Suraju Olaniyi Ogundele Department of Statistics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria
  • Lawrence Chukwudumebi Nzei Department of Statistics, University of Benin, Edo State, Nigeria
  • Friday Ikechukwu Agu Department of Statistics, University of Calabar, Cross-River State, Nigeria

DOI:

https://doi.org/10.13052/jrss0974-8024.1529

Keywords:

Bayesian inference, posterior, prior, regression analysis, rstan package, simulation

Abstract

This article introduced the determination of reliability analysis of the alpha power Gompertz model using the Bayesian techniques. The method developed has been evaluated using women breast cancer in the Stan implementation in R. A survival data used illustrates the proposed Bayesian approach.

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Author Biographies

Joseph Thomas Eghwerido, Department of Statistics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria

Joseph Thomas Eghwerido received his B.Sc. and M.Sc. in Statistics from the Obafemi Awolowo University Ile-Ife in years 2008 and 2013 respectively. He then proceeded to the University of Benin Edo State, Nigeria where he obtained his Ph.D. in Industrial Mathematics with Options in Statistics in 2019. He is the Pioneer and current Head of the Department of Statistics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria. He has several publications in Spatial Statistics, Data Science, Portfolio Management, Probability Theory, and Distribution Theory. He is a member of the Editorial Team of Mathematical Reviews (MathSciNet), Mathematica Slovaca, Scientific African, Thailand Statistician, Fupre Journal of Scientific and Industrial Research, Gazi University Journal of Science, Scientometrics, Austrian Journal of Statistics, and lots more. He is a member of the Nigerian Statistical Association, Nigerian Mathematical Society, and International Biometric Society.

Suraju Olaniyi Ogundele, Department of Statistics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria

Suraju Olaniyi Ogundele received his B.Sc. and M.Sc. in Statistics from the Federal University of Agriculture Abeokuta in years 2002 and the University of Ibadan in 2007 respectively. He then proceeded to the University of Benin Edo State, Nigeria where he obtained his Ph.D. in Industrial Mathematics with Options in Statistics in 2019. He is a lecturer at the Department of Statistics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria. He has several publications in Computational Statistics and Robust Statistical Modelling. He is a member of the Nigerian Statistical Association.

Lawrence Chukwudumebi Nzei, Department of Statistics, University of Benin, Edo State, Nigeria

Lawrence Chukwudumebi Nzei had his B.Sc. Industrial Mathematics from Delta State University, Abraka, Nigeria in 2008 and proceeded to the University of Benin, Benin City where he obtained an M.Sc. Industrial Mathematics (with an option in Statistics) in the year 2015. Currently, Lawrence C. Nzei is a Ph.D. Statistics student in the Department of Statistics, University of Benin, Benin City, Nigeria. He is a Mathematics tutor at the University of Benin Foundation Program. He has several publications in Probability Distribution Theory, Survival analysis and Bayesian analysis. He is also a Reviewer of Thailand Statistician, Pakinstan Journal of Statistics and Operation Research, Gazi University Journal of Science, and lots more. He is a member of the Nigerian Statistical Association, Nigerian Mathematical Society, and International Biometric Society.

Friday Ikechukwu Agu, Department of Statistics, University of Calabar, Cross-River State, Nigeria

Friday Ikechukwu Agu is a Statistician, Researcher, Data Analyst, Academic Adviser, and Lecturer at the Department of Statistics, University of Calabar, Nigeria. He obtained a Bachelor of Science in Mathematics and Statistics from Ebonyi State University, Abakaliki, Nigeria, and a Master of Science in Statistics from the University of Calabar, Calabar, Nigeria. Both programs were completed with research components. Currently, he is a Ph.D. student in statistics. Friday’s research interests include Distribution Theory, Aggregate Claim Modeling in Insurance, Copula, and Financial Tail Dependence. He has published several research articles in high reputable journals. In addition, he is also a reviewer/editor for several academic journals. Friday is a member of the Nigerian Statistical Association and the professional statistician society of Nigeria.

References

AbuJarad, M. H., Khan, A. A., Khaleel, M. A., AbuJarad, E. S. A., AbuJarad, A. H. and Oguntunde, P. E. Bayesian Reliability Analysis of Marshall and Olkin Model. Annals of Data Science, 2019. doi.org/10.1007/s40745-019-00234-3.

AbuJarad, M. H, AbuJarad, E. S. A., and Khan, A. A. Bayesian survival analysis of type I general exponential distributions. Annals of Data Science, 2019. doi.org/10.1007/s40745-019-00228-1.

AbuJarad, M. H. and Khan, A. A. Exponential model: A Bayesian study with Stan. International Journal of Recent Scientific Research 9(8):28495–28506, 2018.

AbuJarad M. H, Khan A. A. Bayesian survival analysis of Topp–Leone generalized family with Stan. Int J Stat Appl 8(5):274–290, 2018a.

Akhtar, M. T., and Khan, A. A. Bayesian analysis of generalized log-Burr family with R. Spinger Plus, 3, 185, 2014. doi: 10.1186/2193-1801-3-185.

Akhtar, M. T. and Khan, A. A. Bayesian reliability analysis of binomial model – Application to success/failure data. Journal of Modern Applied Statistical Methods, 17(2), 2018. eP2623. doi: 10.22237/jmasm/1553803862.

Arora, S. Mahajan, K. K. and Kumari, R. Bayes estimators for the reliability and hazard rate functions of Topp-Leone distribution using Type-II censored data. Communications in Statistics – Simulation and Computation, 2019. doi: 10.1080/03610918.2019.1602646.

Carlin, B. P., and Louis, T. A. Bayesian methods for data analysis. CRC Press, Boca Raton, 2008.

Eghwerido, J. T., Nzei, L. C. and Agu, F. I. The Alpha Power Gompertz Distribution:Characterization, Properties, and Applications. Sankhya A: The Indian Journal of Statistics, 2020. doi.org/10.1007/s13171-020-00198-0.

El-Sayed, M. A., Abd-Elmougod, G. A. and Abdel-Rahman, E. O. Estimation for coefficient of variation of Topp-Leone distribution under adaptive Type-II progressive censoring scheme: Bayesian and non-Bayesian approaches. Journal of Computational and Theoretical Nanoscience 12(11):4028–35, 2015. doi: 10.1166/jctn.2015.4314.

Gelman, A. Prior Distributions for Variance Parameters in Hierarchical Models. Bayesian analysis, 1(3), 515–534, 2006.

Ismail, A. A. Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring, Journal of Statistical Computation and Simulation, 80:11, 1253–1264, 2010. doi: 10.1080/00949650903045058.

Kamar, S. H. Bayesian procedure modified by Fourier series residual to fitting the logistic growth model. Pakistan Journal of Statistics, 35(4), 301–313, 2019.

Khan, N., Akhtar, M. T. and Khan, A. A. Bayesian Analysis of Marshall-Olkin family of distributions, International Journal Recent Scientific Research, 8(7), 18692–18699, 2017.

Khan, N. and Khan, A. A. Bayesian Analysis of Topp-Leone Generalized Exponential Distribution. Austrian Journal of Statistics, 47, 1–15, 2018. doi: 10.17713/ajs.v47i4.716.

Khan, N., Akhtar, M. T., and Khan, A. A. A Bayesian approach to survival analysis of inverse Gaussian model with Laplace approximation. International Journal of Statistics and Applications, 6(6): 391–398. 2016. doi: 10.5923/j.statistics.20160606.08.

Singh, S. K., Singh, U. and Kumar, D. Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors, Journal of Statistical Computation and Simulation, 83(12):2258–69. 2013. doi: 10.1080/00949655.2012.690156.

Sniekers, S. and van der Vaart, A. Adaptive Bayesian credible bands in regression with a Gaussian process prior, Sankhya A: The Indian Journal of Statistics, 2019. doi.org/10.1007/s13171-019-001850.

Turnbull, B. C. and Ghosh, S. K. Unimodal density estimation using Bernstein polynomials, Computational Statistics and Data Analysis, 72, 13–29, 2014.

Yousuf, F. and Khan, A. A. Bayesian Analysis of Normal Model with Stan and Inla. Journal of Emerging Technologies and Innovative Research, 6(6), 406–416, 2019.

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Published

2022-07-27

How to Cite

Eghwerido, J. T. ., Ogundele, S. O. ., Nzei, L. C. ., & Agu, F. I. . (2022). The Bayesian Reliability Analysis of the Alpha Power Gompertz Model. Journal of Reliability and Statistical Studies, 15(02), 617–634. https://doi.org/10.13052/jrss0974-8024.1529

Issue

2022: Vol 15 Iss 2

Section

Articles