A new bivariate Kumaraswamy discrete Lindley model: theory and multidisciplinary data analysis

i

This article has been updated. A Correction to this article was published on .

i

The Original Article was published on

i

The Original Article was published on

i

This article has been updated

i

This article was retracted on

i

This article has been updated

Abstract

This study presents the bivariate Kumaraswamy discrete Lindley distribution, developed via a trivariate minimization framework. The model features closed-form formulas for its joint survival, cumulative distribution, and probability mass functions, enabling efficient computer implementation. We analyze the identifiability of the suggested model and the positive dependence structure, deriving the joint probability generating function and conditional expectations. The joint hazard rate function demonstrates considerable distributional flexibility, allowing for monotonic, bathtub, and unimodal shapes. Subsequent to the derivation of maximum likelihood estimators and the Fisher information matrix, we conduct simulation investigations across several sample sizes. The suggested model, when applied to three authentic datasets from the healthcare and manufacturing sectors, demonstrates a better fit than competitive models based on standard statistical selection criteria, confirming its efficacy for modeling count data.

Keywords

statistical model / conditional expectation / simulation / sustainable practices / statistics and numerical data

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org

References

[1] M. El-Morshedy, M. S. Eliwa, A. Tyagi, H. S. Shahen, A discrete extension of the Lindley distribution for health and sustainability data: Theoretical insights and decision-making applications, Partial Differ. Equations Appl. Math., 13 (2025), 101013. https://doi.org/10.1016/j.padiff.2024.101013

[2] V. E. Piperigou, H. Papageorgiou, On truncated bivariate discrete distributions: A unified treatment, Metrika, 58 (2003), 221-233. https://doi.org/10.1007/s001840200239

[3] C. S. Davis, Statistical methods for the analysis of repeated measurements, Springer, New York, 2002. https://link.springer.com/book/10.1007/b97287

[4] A. W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84 (1997), 641-652. https://doi.org/10.1093/biomet/84.3.641

[5] H. Lee, J. H. Cha, On two general classes of discrete bivariate distributions, Am. Stat., 69 (2015), 221-230. https://doi.org/10.1080/00031305.2015.1044564

[6] M. Goff, Multivariate Discrete Phase-Type Distributions , Ph.D. Thesis, Washington State University, 2001. Available from: https://hdl.handle.net/2376/303.

[7] M. El-Dawoody, M. S. Eliwa, Bivariate discrete burr lifetime distribution: A mathematical and statistical framework for modeling medical and engineering data, Inf. Sci. Lett., 12 (2023), 3199-3214. https://doi.org/10.18576/isl/121129

[8] V. Nekoukhou, D. Kundu, Bivariate discrete generalized exponential distribution, Statistics, 51 (2017), 1143-1158. https://doi.org/10.1080/02331888.2017.1289534

[9] D. Kundu, V. Nekoukhou, On bivariate discrete Weibull distribution, Commun. Stat.- Theory Methods, 48 (2019), 3464-3481. https://doi.org/10.1080/03610926.2018.1476712

[10] M. S. Eliwa, M. El-Morshedy, Bayesian and non-Bayesian estimation of four-parameter of bivariate discrete inverse Weibull distribution with applications to model failure times, football, and biological data, Filomat, 34 (2020), 2511-2531. https://doi.org/10.2298/FIL2008511E

[11] A. Barbiero, Discrete analogues of continuous bivariate probability distributions, Ann. Oper. Res., 312 (2022), 23-43. https://doi.org/10.1007/s10479-019-03388-8

[12] Y. M. Amer, D. Abdelhady, R. M. Shalabi, A novel family of continuous-discrete bivariate distributions, Comput. J. Math. Stat. Sci., 5 (2026), 415-437. https://doi.org/10.21608/cjmss.2025.405765.1233

[13] S. Kocherlakota, K. Kocherlakota, Bivariate discrete distributions, CRC Press, 2017. https://doi.org/10.1201/9781315138480

[14] I. McHale, P. Scarf, Modelling soccer matches using bivariate discrete distributions with general dependence structure, Stat. Neerl., 61 (2007), 432-445. https://doi.org/10.1111/j.1467-9574.2007.00368.x

[15] H. Lee, J. H. Cha, New discrete bivariate distributions generated from discrete time point process model, Methodol. Comput. Appl. Probab., 28 (2026), 41. https://doi.org/10.1007/s11009-026-10263-0

[16] M. J. Lee, N. Y. Yoo, J. H. Cha, A new general class of discrete bivariate distributions constructed by the usual stochastic order, Am. Stat., 79 (2025), 449-466. https://doi.org/10.1080/00031305.2025.2486306

[17] J. Aitchison, C. H. Ho, The multivariate Poisson-log normal distribution, Biometrika, 76 (1989), 643-653. https://doi.org/10.1093/biomet/76.4.643