IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i21p3401-d1510614.html
   My bibliography  Save this article

Discrete Joint Random Variables in Fréchet-Weibull Distribution: A Comprehensive Mathematical Framework with Simulations, Goodness-of-Fit Analysis, and Informed Decision-Making

Author

Listed:
  • Diksha Das

    (Department of Statistics, North-Eastern Hill University, Meghalaya 793022, India)

  • Tariq S. Alshammari

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Khudhayr A. Rashedi

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Bhanita Das

    (Department of Statistics, North-Eastern Hill University, Meghalaya 793022, India)

  • Partha Jyoti Hazarika

    (Department of Statistics, Dibrugarh University, Assam 786004, India)

  • Mohamed S. Eliwa

    (Department of Statistics and Operations Research, College of Science, Qassim University, Saudi Arabia)

Abstract

This paper introduces a novel four-parameter discrete bivariate distribution, termed the bivariate discretized Fréchet–Weibull distribution (BDFWD), with marginals derived from the discretized Fréchet–Weibull distribution. Several statistical and reliability properties are thoroughly examined, including the joint cumulative distribution function, joint probability mass function, joint survival function, bivariate hazard rate function, and bivariate reversed hazard rate function, all presented in straightforward forms. Additionally, properties such as moments and their related concepts, the stress–strength model, total positivity of order 2, positive quadrant dependence, and the median are examined. The BDFWD is capable of modeling asymmetric dispersion data across various forms of hazard rate shapes and kurtosis. Following the introduction of the mathematical and statistical frameworks of the BDFWD, the maximum likelihood estimation approach is employed to estimate the model parameters. A simulation study is also conducted to investigate the behavior of the generated estimators. To demonstrate the capability and flexibility of the BDFWD, three distinct datasets are analyzed from various fields, including football score records, recurrence times to infection for kidney dialysis patients, and student marks from two internal examination statistical papers. The study confirms that the BDFWD outperforms competitive distributions in terms of efficiency across various discrete data applications.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3401-:d:1510614
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/21/3401/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/21/3401/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Debasis Kundu & Vahid Nekoukhou, 2019. "On bivariate discrete Weibull distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(14), pages 3464-3481, July.
    2. C. Satheesh Kumar, 2008. "A unified approach to bivariate discrete distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 113-123, January.
    3. Kemp, Adrienne W., 2013. "New discrete Appell and Humbert distributions with relevance to bivariate accident data," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 2-6.
    4. Kundu, Debasis & Gupta, Rameshwar D., 2009. "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 581-593, April.
    5. 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.
    6. Hyunju Lee & Ji Hwan Cha, 2015. "On Two General Classes of Discrete Bivariate Distributions," The American Statistician, Taylor & Francis Journals, vol. 69(3), pages 221-230, August.
    7. K. Jose & Miroslav Ristić & Ancy Joseph, 2011. "Marshall–Olkin bivariate Weibull distributions and processes," Statistical Papers, Springer, vol. 52(4), pages 789-798, November.
    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. Debasis Kundu, 2020. "On a General Class of Discrete Bivariate Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 270-304, November.
    2. Debasis Kundu, 2022. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 575-595, November.
    3. Debasis Kundu, 2021. "Stationary GE-Process and its Application in Analyzing Gold Price Data," Papers 2201.02568, arXiv.org.
    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. 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.
    9. Isidro Jesús González-Hernández & Rafael Granillo-Macías & Carlos Rondero-Guerrero & Isaías Simón-Marmolejo, 2021. "Marshall-Olkin distributions: a bibliometric study," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(11), pages 9005-9029, November.
    10. 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.
    11. 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.
    12. Kumar C. Satheesh, 2013. "The Bivariate Confluent Hypergeometric Series Distribution and Some of Its Properties," Stochastics and Quality Control, De Gruyter, vol. 28(1), pages 23-30, October.
    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. 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.
    15. Mercier, Sophie & Pham, Hai Ha, 2017. "A bivariate failure time model with random shocks and mixed effects," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 33-51.
    16. 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.
    17. Kundu, Debasis & Gupta, Arjun K., 2014. "On bivariate Weibull-Geometric distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 19-29.
    18. Denys Pommeret, 2013. "A two-sample test when data are contaminated," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 501-516, November.
    19. 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.
    20. Attila Csenki, 2015. "A Differential Equation for a Class of Discrete Lifetime Distributions with an Application in Reliability," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 647-660, 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:21:p:3401-:d:1510614. 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.