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A New Bivariate Distribution With Applications on Dependent Competing Risks Data

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  • Thamer Manshi
  • Ammar M. Sarhan
  • Bruce Smith

Abstract

A new bivariate distribution is proposed in this paper using the univariate modified Weibull extension distribution. The proposed distribution is referred to as the bivariate Modified Weibull Extension (BMWE) distribution. The BMWE distribution is of Marshall-Olkin type. We discuss some of the statistical properties of the BMWE distribution. Applications of this distribution to dependent competing risks data are discussed. The maximum likelihood estimators (MLE) of the model parameters using both bivariate data and dependent competing risks data are discussed. These MLE's cannot be obtained in closed form. Therefore, numerical optimization methods are applied. A simulation study is carried out to investigate the performance of the estimation technique. Two real data sets; one bivariate data set and another dependent competing risks data set, are analyzed using the proposed distribution for illustrative and comparison purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:ibn:ijspjl:v:12:y:2025:i:3:p:27
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    References listed on IDEAS

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    1. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    2. 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.
    3. Kundu, Debasis & Gupta, Rameshwar D., 2009. "Bivariate generalized exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 581-593, April.
    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. 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. Sarhan, Ammar M. & Apaloo, Joseph, 2013. "Exponentiated modified Weibull extension distribution," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 137-144.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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