IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i12p1774-d1410459.html
   My bibliography  Save this article

Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

Author

Listed:
  • Ehab M. Almetwally

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
    Department of Statistics, Faculty of Business Administration, Delta University for Science and Technology, Gamasa 11153, Egypt)

  • Aisha Fayomi

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Maha E. Qura

    (Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt)

Abstract

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology’s applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients.

Suggested Citation

  • Ehab M. Almetwally & Aisha Fayomi & Maha E. Qura, 2024. "Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings," Mathematics, MDPI, vol. 12(12), pages 1-35, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1774-:d:1410459
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/12/1774/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/12/1774/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rainer Winkelmann, 2012. "Copula Bivariate Probit Models: With An Application To Medical Expenditures," Health Economics, John Wiley & Sons, Ltd., vol. 21(12), pages 1444-1455, December.
    2. Hiba Z. Muhammed & Ehab M. Almetwally, 2023. "Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution Under Progressive Type-II Censoring," Annals of Data Science, Springer, vol. 10(2), pages 481-512, April.
    3. Aisha Fayomi & Ehab M. Almetwally & Maha E. Qura, 2023. "Exploring New Horizons: Advancing Data Analysis in Kidney Patient Infection Rates and UEFA Champions League Scores Using Bivariate Kavya–Manoharan Transformation Family of Distributions," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    4. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    5. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    6. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    7. Hanan Haj Ahmad & Ehab M. Almetwally & Dina A. Ramadan, 2023. "Investigating the Relationship between Processor and Memory Reliability in Data Science: A Bivariate Model Approach," Mathematics, MDPI, vol. 11(9), pages 1-23, 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. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    2. Quessy, Jean-François, 2021. "A Szekely–Rizzo inequality for testing general copula homogeneity hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    3. Elisa Luciano & Jaap Spreeuw & Elena Vigna, 2012. "Evolution of coupled lives' dependency across generations and pricing impact," Carlo Alberto Notebooks 258, Collegio Carlo Alberto.
    4. Miriam Jaser & Aleksey Min, 2021. "On tests for symmetry and radial symmetry of bivariate copulas towards testing for ellipticity," Computational Statistics, Springer, vol. 36(3), pages 1-26, September.
    5. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    6. Pravin Trivedi & David Zimmer, 2017. "A Note on Identification of Bivariate Copulas for Discrete Count Data," Econometrics, MDPI, vol. 5(1), pages 1-11, February.
    7. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    8. Zheng Wei & Seongyong Kim & Boseung Choi & Daeyoung Kim, 2019. "Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 365-387, January.
    9. Brodsky, Boris & Penikas, Henry & Safaryan, Irina, 2009. "Detection of Structural Breaks in Copula Models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 16(4), pages 3-15.
    10. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    11. Marra Giampiero & Radice Rosalba, 2017. "A joint regression modeling framework for analyzing bivariate binary data in R," Dependence Modeling, De Gruyter, vol. 5(1), pages 268-294, December.
    12. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    13. Boris Brodsky & Henry Penikas & Irina Safaryan, 2012. "Copula structural shift identification," HSE Working papers WP BRP 05/FE/2012, National Research University Higher School of Economics.
    14. Kateryna Tkach & Chiara Gigliarano, 2018. "Multidimensional poverty measurement: dependence between well-being dimensions using copula function," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 72(3), pages 89-100, July-Sept.
    15. Hua, Lei & Polansky, Alan & Pramanik, Paramahansa, 2019. "Assessing bivariate tail non-exchangeable dependence," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    16. Mangold, Benedikt, 2017. "New concepts of symmetry for copulas," FAU Discussion Papers in Economics 06/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics, revised 2017.
    17. Kojadinovic, Ivan, 2017. "Some copula inference procedures adapted to the presence of ties," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 24-41.
    18. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    19. Almeida, Carlos & Czado, Claudia, 2012. "Efficient Bayesian inference for stochastic time-varying copula models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1511-1527.
    20. Lawless, Jerald F. & Yilmaz, Yildiz E., 2011. "Comparison of semiparametric maximum likelihood estimation and two-stage semiparametric estimation in copula models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2446-2455, July.
    21. repec:jss:jstsof:34:i09 is not listed on IDEAS
    22. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.

    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:gam:jmathe:v:12:y:2024:i:12:p:1774-:d:1410459. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.