A thorough examination of the bivariate Kimeldorf-Sampson extended Weibull family in light of versatile statistical applications

M. A. Alawady; H. M. Barakat; M. J. A. Alrawashdeh; D. A. Abd El-Rahman; I. A. Husseiny; M. A. Alawady; H. M. Barakat; M. J. A. Alrawashdeh; D. A. Abd El-Rahman; I. A. Husseiny

doi:10.3934/math.2026375

AIMS Mathematics

2026, Volume 11, Issue 4: 9093-9125. doi: 10.3934/math.2026375

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A thorough examination of the bivariate Kimeldorf-Sampson extended Weibull family in light of versatile statistical applications

1.
Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
3.
Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt

Received: 31 January 2026 Revised: 09 March 2026 Accepted: 13 March 2026 Published: 02 April 2026
MSC : 60B12, 62G30

Families of bivariate distributions with weak dependence between their margins are of practical importance, despite being relatively uncommon. These families can be constructed using specific copulas. This paper introduces a new family, KSEW, developed using the bivariate Kimeldorf-Sampson (KS) copula and the extended Weibull (EW) distributions. The KSEW family is designed for applications requiring marginal distributions with low but significant levels of dependence, positioned above the threshold of independence. Key properties of the KSEW family were derived, including product moments and the correlation coefficient. The study also explored the uniform, power, Weibull, Rayleigh, exponential, and Lomax distributions as specific cases within the EW family, identifying the maximum correlation coefficient for each. Additionally, the reliability function in the dependent stress-strength model under the KS framework was developed. The concomitants of order statistics and associated information measures using the KSEW distribution were also investigated. The practical applicability of the KSEW family was demonstrated through analysis of two real-world datasets, highlighting its suitability for scenarios involving weakly dependent random variables.
- Kimeldorf-Sampson family,
- extended Weibull distribution,
- concomitants,
- simulation,
- order statistics,
- Shannon entropy,
- extropy
Citation: M. A. Alawady, H. M. Barakat, M. J. A. Alrawashdeh, D. A. Abd El-Rahman, I. A. Husseiny. A thorough examination of the bivariate Kimeldorf-Sampson extended Weibull family in light of versatile statistical applications[J]. AIMS Mathematics, 2026, 11(4): 9093-9125. doi: 10.3934/math.2026375

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Abstract

Families of bivariate distributions with weak dependence between their margins are of practical importance, despite being relatively uncommon. These families can be constructed using specific copulas. This paper introduces a new family, KSEW, developed using the bivariate Kimeldorf-Sampson (KS) copula and the extended Weibull (EW) distributions. The KSEW family is designed for applications requiring marginal distributions with low but significant levels of dependence, positioned above the threshold of independence. Key properties of the KSEW family were derived, including product moments and the correlation coefficient. The study also explored the uniform, power, Weibull, Rayleigh, exponential, and Lomax distributions as specific cases within the EW family, identifying the maximum correlation coefficient for each. Additionally, the reliability function in the dependent stress-strength model under the KS framework was developed. The concomitants of order statistics and associated information measures using the KSEW distribution were also investigated. The practical applicability of the KSEW family was demonstrated through analysis of two real-world datasets, highlighting its suitability for scenarios involving weakly dependent random variables.

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