IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v13y2022i2d10.1007_s13198-021-01348-9.html
   My bibliography  Save this article

Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions

Author

Listed:
  • Mehdi Basikhasteh

    (Islamic Azad University)

  • Iman Makhdoom

    (Payame Noor University(PNU))

Abstract

The bivariate Weibull-Geometric (BWG) distribution has been proposed by Kundu and Gupta (J Multivar Anal 123:19-29, 2014). They derived different properties of the proposed distribution and computing the maximum likelihood estimators via the expectation-maximization algorithm. The Bayes estimators of the parameters from the BWG distribution based on the squared error loss function (symmetric) and linear-exponential (LINEX) loss function (asymmetric), using informative and non-informative gamma priors are presented. Since the Bayes estimators of the mentioned distribution with five parameters cannot be obtained in explicit forms; the Gibbs sampler procedure is opted to achieve the Bayes estimators. Markov Chain Monte Carlo (MCMC) methods are broadly used to implement and compute the Bayes estimates. The convergence of the Markov chain to a stationary distribution has also been considered in detail. The associated credible intervals, namely the highest posterior density of the unknown parameters, are also constructed. The Monte Carlo simulations are done to compare different estimates. Finally, a real data set is considered to perform for illustrative purposes.

Suggested Citation

  • Mehdi Basikhasteh & Iman Makhdoom, 2022. "Bayesian inference of bivariate Weibull geometric model based on LINEX and quadratic loss functions," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 867-880, April.
    • Handle: RePEc:spr:ijsaem:v:13:y:2022:i:2:d:10.1007_s13198-021-01348-9
    DOI: 10.1007/s13198-021-01348-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-021-01348-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13198-021-01348-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Philip Heidelberger & Peter D. Welch, 1983. "Simulation Run Length Control in the Presence of an Initial Transient," Operations Research, INFORMS, vol. 31(6), pages 1109-1144, December.
    2. David D. Hanagal & Richa Sharma, 2015. "Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 24-47, January.
    3. Barreto-Souza, Wagner, 2012. "Bivariate gamma-geometric law and its induced Lévy process," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 130-145.
    4. G. Heinrich & U. Jensen, 1995. "Parameter estimation for a bivariate lifetime distribution in reliability with multivariate extensions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 49-65, December.
    5. Sarhan, Ammar M. & Balakrishnan, N., 2007. "A new class of bivariate distributions and its mixture," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1508-1527, August.
    6. Franco, Manuel & Vivo, Juana-María, 2010. "A multivariate extension of Sarhan and Balakrishnan's bivariate distribution and its ageing and dependence properties," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 491-499, March.
    7. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    8. M. E. Ghitany & E. K. Al-Hussaini & R. A. Al-Jarallah, 2005. "Marshall-Olkin extended weibull distribution and its application to censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1025-1034.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    2. Calabrese, Raffaella & Osmetti, Silvia Angela, 2019. "A new approach to measure systemic risk: A bivariate copula model for dependent censored data," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1053-1064.
    3. Muhammad H. Tahir & Muhammad Adnan Hussain & Gauss M. Cordeiro & M. El-Morshedy & M. S. Eliwa, 2020. "A New Kumaraswamy Generalized Family of Distributions with Properties, Applications, and Bivariate Extension," Mathematics, MDPI, vol. 8(11), pages 1-28, November.
    4. Muhammad Mohsin & Hannes Kazianka & Jürgen Pilz & Albrecht Gebhardt, 2014. "A new bivariate exponential distribution for modeling moderately negative dependence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 123-148, March.
    5. Rakesh Ranjan & Vastoshpati Shastri, 2019. "Posterior and predictive inferences for Marshall Olkin bivariate Weibull distribution via Markov chain Monte Carlo methods," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(6), pages 1535-1543, December.
    6. Paul Hewson & Keming Yu, 2008. "Quantile regression for binary performance indicators," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(5), pages 401-418, September.
    7. Hancock, Joana & Vieira, Sara & Lima, Hipólito & Schmitt, Vanessa & Pereira, Jaconias & Rebelo, Rui & Girondot, Marc, 2019. "Overcoming field monitoring restraints in estimating marine turtle internesting period by modelling individual nesting behaviour using capture-mark-recapture data," Ecological Modelling, Elsevier, vol. 402(C), pages 76-84.
    8. Lada, Emily K. & Wilson, James R., 2006. "A wavelet-based spectral procedure for steady-state simulation analysis," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1769-1801, November.
    9. Enver Yücesan, 1993. "Randomization tests for initialization bias in simulation output," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(5), pages 643-663, August.
    10. Boikanyo Makubate & Fastel Chipepa & Broderick Oluyede & Peter O. Peter, 2021. "The Marshall-Olkin Half Logistic-G Family of Distributions With Applications," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 10(2), pages 120-120, March.
    11. Riccardo (Jack) Lucchetti & Luca Pedini, 2020. "ParMA: Parallelised Bayesian Model Averaging for Generalised Linear Models," Working Papers 2020:28, Department of Economics, University of Venice "Ca' Foscari".
    12. Burda Martin & Bélisle Louis, 2019. "Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo," Dependence Modeling, De Gruyter, vol. 7(1), pages 133-149, January.
    13. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    14. Yu, Jun, 2012. "A semiparametric stochastic volatility model," Journal of Econometrics, Elsevier, vol. 167(2), pages 473-482.
    15. Goldman Elena & Tsurumi Hiroki, 2005. "Bayesian Analysis of a Doubly Truncated ARMA-GARCH Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(2), pages 1-38, June.
    16. Erhard Cramer & Udo Kamps, 2001. "Estimation with Sequential Order Statistics from Exponential Distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 307-324, June.
    17. Andr'es Ram'irez-Hassan & Alejandro L'opez-Vera, 2021. "Semi-parametric estimation of the EASI model: Welfare implications of taxes identifying clusters due to unobserved preference heterogeneity," Papers 2109.07646, arXiv.org.
    18. Hadeel S Klakattawi, 2022. "Survival analysis of cancer patients using a new extended Weibull distribution," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-20, February.
    19. Christian Hering & Jan-Frederik Mai, 2012. "Moment-based estimation of extendible Marshall-Olkin copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 601-620, July.
    20. Saralees Nadarajah & Božidar Popović & Miroslav Ristić, 2013. "Compounding: an R package for computing continuous distributions obtained by compounding a continuous and a discrete distribution," Computational Statistics, Springer, vol. 28(3), pages 977-992, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:ijsaem:v:13:y:2022:i:2:d:10.1007_s13198-021-01348-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.