IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v86y2024i1d10.1007_s13171-023-00314-w.html
   My bibliography  Save this article

A Bivariate Teissier Distribution: Properties, Bayes Estimation and Application

Author

Listed:
  • Vikas Kumar Sharma

    (Banaras Hindu University)

  • Sudhanshu Vikram Singh

    (Institute of Infrastructure Techonology Research And Management)

  • Ashok Kumar Pathak

    (Central University of Panjab)

Abstract

This article presents a bivariate extension of the Teissier distribution, whose univariate marginal distributions belong to the exponentiated Teissier family. Analytic expressions for the different statistical quantities such as conditional distribution, joint moments, and quantile function are explicitly derived. For the proposed distribution, the concepts of reliability and dependence measures are also explored in details. Both the maximum likelihood technique and the Bayesian approach are utilised in the process of parameter estimation for the proposed distribution with unknown parameters. Several numerical experiments are reported to study the performance of the classical and Bayes estimators for varying sample size. Finally, a bivariate data is fitted using the proposed distribution to show its applicability over the bivariate exponential, Rayleigh, and linear exponential distributions in real-life situations.

Suggested Citation

  • Vikas Kumar Sharma & Sudhanshu Vikram Singh & Ashok Kumar Pathak, 2024. "A Bivariate Teissier Distribution: Properties, Bayes Estimation and Application," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 67-92, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00314-w
    DOI: 10.1007/s13171-023-00314-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-023-00314-w
    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/s13171-023-00314-w?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. Pillai, R. N. & Jayakumar, K., 1995. "Discrete Mittag-Leffler distributions," Statistics & Probability Letters, Elsevier, vol. 23(3), pages 271-274, May.
    2. Balakrishnapillai Vineshkumar & Narayanan Unnikrishnan Nair, 2019. "Bivariate Quantile Functions and their Applications to Reliability Modelling," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 3-21.
    3. A. Dolati & M. Amini & S. Mirhosseini, 2014. "Dependence properties of bivariate distributions with proportional (reversed) hazards marginals," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 333-347, April.
    4. Johnson, N. L. & Kotz, Samuel, 1975. "A vector multivariate hazard rate," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 53-66, March.
    5. N. Balakrishnan & Debasis Kundu, 2019. "Birnbaum‐Saunders distribution: A review of models, analysis, and applications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(1), pages 4-49, January.
    6. Naderi, Mehrdad & Hashemi, Farzane & Bekker, Andriette & Jamalizadeh, Ahad, 2020. "Modeling right-skewed financial data streams: A likelihood inference based on the generalized Birnbaum–Saunders mixture model," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    7. Vikas Kumar Sharma & Sudhanshu V. Singh & Komal Shekhawat, 2022. "Exponentiated Teissier distribution with increasing, decreasing and bathtub hazard functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(2), pages 371-393, January.
    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. 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.
    2. Shikhar Tyagi, 2024. "On bivariate Teissier model using Copula: dependence properties, and case studies," 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. 15(6), pages 2483-2499, June.
    3. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
    4. Saulo, Helton & Balakrishnan, Narayanaswamy & Vila, Roberto, 2023. "On a quantile autoregressive conditional duration model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 425-448.
    5. M. Shafaei Noughabi & M. Kayid, 2019. "Bivariate quantile residual life: a characterization theorem and statistical properties," Statistical Papers, Springer, vol. 60(6), pages 2001-2012, December.
    6. Emad-Eldin Aly & Nadjib Bouzar, 2000. "On Geometric Infinite Divisibility and Stability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 790-799, December.
    7. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2023. "The tenets of quantile-based inference in Bayesian models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    8. Chanseok Park & Min Wang, 2024. "Parameter Estimation of Birnbaum-Saunders Distribution under Competing Risks Using the Quantile Variant of the Expectation-Maximization Algorithm," Mathematics, MDPI, vol. 12(11), pages 1-17, June.
    9. Shaomin Wu & Hongyan Dui & Linmin Hu, 2024. "Construction of copulas for bivariate failure rates," Annals of Operations Research, Springer, vol. 341(2), pages 1177-1189, October.
    10. P. Sankaran & K. Jayakumar, 2008. "On proportional odds models," Statistical Papers, Springer, vol. 49(4), pages 779-789, October.
    11. Nazarizadeh, Farzaneh & Alemtabriz, Akbar & Zandieh, Mostafa & Raad, Abbas, 2022. "An analytical model for reliability assessment of the rail system considering dependent failures (case study of Iranian railway)," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    12. S.M. Sunoj & N. Unnikrishnan Nair, 1999. "Bivariate distributions with weighted marginals and reliablity modelling," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 118-126.
    13. Buddana Amrutha & Kozubowski Tomasz J., 2014. "Discrete Pareto Distributions," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 143-156, December.
    14. 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.
    15. Belzunce, Félix & Mercader, José A. & Ruiz, José M., 2003. "Multivariate aging properties of epoch times of nonhomogeneous processes," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 335-350, February.
    16. Indranil Ghosh & Osborne Banks, 2021. "A Study of Bivariate Generalized Pareto Distribution and its Dependence Structure Among Model Parameters," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 575-604, November.
    17. Hossein Pasha-Zanoosi, 2024. "Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 570-602, June.
    18. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    19. Kalanka P. Jayalath, 2021. "Fiducial Inference on the Right Censored Birnbaum–Saunders Data via Gibbs Sampler," Stats, MDPI, vol. 4(2), pages 1-15, May.
    20. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.

    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:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00314-w. 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.