IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i4d10.1007_s11009-023-10061-y.html
   My bibliography  Save this article

Bivariate Semi-Parametric Model: Bayesian Inference

Author

Listed:
  • Debashis Samanta

    (Aliah University)

  • Debasis Kundu

    (Indian Institute of Technology Kanpur)

Abstract

The motivation of this paper came from two bivariate diabetic retinopathy data sets. The main aim is to test whether the laser treatment delays the onset of blindness compared to the traditional treatment. The first data set is of 197 patients and it provides the onset of blindness of the two eyes. The observed data are heavily censored on both the variables. The second data set is of 91 patients, and it indicates the minimum time of the onset of blindness between the two eyes. In both the cases there is a significant proportion where the onset of blindness has occured on both the eyes simultaneously, i.e. there is a significant proportion where both the variables are equal. Hence, the two variables cannot be treated as independent. We have used a Marshall-Olkin bivariate exponential or Weibull type a bivariate semi-parametric model, where the base line distribution is more flexible than any parametric distribution. The base line distribution is assumed to have a piecewise constant hazard function and that makes the Bayes line hazard function to be very flexible. Marshall-Olkin bivariate exponential distribution becomes a special case of the model. The maximum likelihood estimators may not always exist, and we have considered the Bayesian inference of the unknown parameters. We have used importance sampling technique to compute Bayes estimators and the associated credible intervals. We have addressed some testing of hypothesis problem also based on Bayes factors. Finally, both the data sets have been analyzed, and it is observed for one data set the laser treatment has a significantly different effect than the traditional treatment, where as for the other data set no significantly different effect has been observed.

Suggested Citation

  • Debashis Samanta & Debasis Kundu, 2023. "Bivariate Semi-Parametric Model: Bayesian Inference," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-23, December.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:4:d:10.1007_s11009-023-10061-y
    DOI: 10.1007/s11009-023-10061-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10061-y
    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/s11009-023-10061-y?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. Kundu, Debasis & Dey, Arabin Kumar, 2009. "Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 956-965, February.
    2. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    3. Melody S. Goodman & Yi Li & Ram C. Tiwari, 2011. "Detecting multiple change points in piecewise constant hazard functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2523-2532, January.
    4. 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.
    5. Feizjavadian, S.H. & Hashemi, R., 2015. "Analysis of dependent competing risks in the presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 19-34.
    6. Kundu, Debasis & Gupta, Rameshwar D., 2009. "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 581-593, April.
    7. Sarhan, Ammar M. & Hamilton, David C. & Smith, Bruce & Kundu, Debasis, 2011. "The bivariate generalized linear failure rate distribution and its multivariate extension," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 644-654, January.
    8. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    9. Murphy, Anthony, 1996. "A piecewise-constant hazard-rate model for the duration of unemployment in single-interview samples of the stock of unemployed," Economics Letters, Elsevier, vol. 51(2), pages 177-183, May.
    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. Thamer Manshi & Ammar M. Sarhan & Bruce Smith, 2025. "A New Bivariate Distribution With Applications on Dependent Competing Risks Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 12(3), pages 1-27, January.
    2. Debasis Kundu, 2024. "A Stationary Proportional Hazard Class Process and its Applications," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-21, December.
    3. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    4. M. S. Eliwa & M. El-Morshedy, 2019. "Bivariate Gumbel-G Family of Distributions: Statistical Properties, Bayesian and Non-Bayesian Estimation with Application," Annals of Data Science, Springer, vol. 6(1), pages 39-60, March.
    5. 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.
    6. Li, Yang & Sun, Jianguo & Song, Shuguang, 2012. "Statistical analysis of bivariate failure time data with Marshall–Olkin Weibull models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 2041-2050.
    7. Muhammed, Hiba Z., 2020. "On a bivariate generalized inverted Kumaraswamy distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    8. 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.
    9. Kundu, Debasis & Franco, Manuel & Vivo, Juana-Maria, 2014. "Multivariate distributions with proportional reversed hazard marginals," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 98-112.
    10. Wang, Liang & Tripathi, Yogesh Mani & Dey, Sanku & Zhang, Chunfang & Wu, Ke, 2022. "Analysis of dependent left-truncated and right-censored competing risks data with partially observed failure causes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 285-307.
    11. Sofian T. Obeidat & Diksha Das & Mohamed S. Eliwa & Bhanita Das & Partha Jyoti Hazarika & Wael W. Mohammed, 2025. "Two-Dimensional Probability Models for the Weighted Discretized Fréchet–Weibull Random Variable with Min–Max Operators: Mathematical Theory and Statistical Goodness-of-Fit Analysis," Mathematics, MDPI, vol. 13(4), pages 1-29, February.
    12. 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.
    13. S. Mirhosseini & M. Amini & D. Kundu & A. Dolati, 2015. "On a new absolutely continuous bivariate generalized exponential distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 61-83, March.
    14. 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.
    15. Sarhan, Ammar M. & Hamilton, David C. & Smith, Bruce & Kundu, Debasis, 2011. "The bivariate generalized linear failure rate distribution and its multivariate extension," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 644-654, January.
    16. Debasis Kundu, 2022. "Bivariate Semi-parametric Singular Family of Distributions and its Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 846-872, November.
    17. Diksha Das & Tariq S. Alshammari & Khudhayr A. Rashedi & Bhanita Das & Partha Jyoti Hazarika & Mohamed S. Eliwa, 2024. "Discrete Joint Random Variables in Fréchet-Weibull Distribution: A Comprehensive Mathematical Framework with Simulations, Goodness-of-Fit Analysis, and Informed Decision-Making," Mathematics, MDPI, vol. 12(21), pages 1-28, October.
    18. Manuel Franco & Juana-María Vivo & Debasis Kundu, 2020. "A Generator of Bivariate Distributions: Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(10), pages 1-30, October.
    19. 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.
    20. 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.

    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:metcap:v:25:y:2023:i:4:d:10.1007_s11009-023-10061-y. 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.