Uncertainty measures for concomitants of upper $ k $-record values based on the Huang-Kotz-Morgenstern type Ⅱ family

G. M. Mansour; H. M. Barakat; M. A. Alawady; M. A. Abd Elgawad; H. N. Alqifari; T. S. Taher; A. H. Syam; G. M. Mansour; H. M. Barakat; M. A. Alawady; M. A. Abd Elgawad; H. N. Alqifari; T. S. Taher; A. H. Syam

doi:10.3934/math.20251279

AIMS Mathematics

2025, Volume 10, Issue 12: 29071-29106. doi: 10.3934/math.20251279

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Uncertainty measures for concomitants of upper $ k $-record values based on the Huang-Kotz-Morgenstern type Ⅱ family

1.
Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt
2.
Department of Statistics and Operations Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
3.
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
4.
Higher Technological Institute at 10th of Ramadan City, Egypt
5.
Department of Mathematics and Computer Science, Faculty of Science, Benha University, Benha 13518, Egypt

Received: 13 October 2025 Revised: 24 November 2025 Accepted: 01 December 2025 Published: 11 December 2025
MSC : 60B12, 62G30

Statistical models involving bivariate data are among the most important areas of statistical theory. Concomitants of $ k $-record values (CKR) are key topics in statistical theory that have not been extensively studied by researchers. In this paper, we derived the marginal distribution of CKR based on the Huang-Kotz Farlie-Gumbel-Morgenstern type Ⅱ (HK–FGM2) family of bivariate distributions. Additionally, we obtained an expression for past extropy associated with the CKR within the HK–FGM2 family. Three related uncertainty measures (the cumulative residual extropy (CREX), cumulative extropy (CEX), and the negative cumulative extropy (NCEX)), were formulated for CKR based on this family. Furthermore, estimation techniques for CREX and NCEX were explored by employing empirical estimators tailored to CKR using the HK–FGM2 family. Finally, we analyzed a computer series system dataset for illustration purposes, providing significant insights into the behavior of CKR uncertainty measures.
- HK-FGM family,
- concomitants,
- k-record values,
- entropy,
- past extropy,
- cumulative extropy,
- cumulative residual extropy
Citation: G. M. Mansour, H. M. Barakat, M. A. Alawady, M. A. Abd Elgawad, H. N. Alqifari, T. S. Taher, A. H. Syam. Uncertainty measures for concomitants of upper $ k $-record values based on the Huang-Kotz-Morgenstern type Ⅱ family[J]. AIMS Mathematics, 2025, 10(12): 29071-29106. doi: 10.3934/math.20251279

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Abstract

Statistical models involving bivariate data are among the most important areas of statistical theory. Concomitants of $ k $-record values (CKR) are key topics in statistical theory that have not been extensively studied by researchers. In this paper, we derived the marginal distribution of CKR based on the Huang-Kotz Farlie-Gumbel-Morgenstern type Ⅱ (HK–FGM2) family of bivariate distributions. Additionally, we obtained an expression for past extropy associated with the CKR within the HK–FGM2 family. Three related uncertainty measures (the cumulative residual extropy (CREX), cumulative extropy (CEX), and the negative cumulative extropy (NCEX)), were formulated for CKR based on this family. Furthermore, estimation techniques for CREX and NCEX were explored by employing empirical estimators tailored to CKR using the HK–FGM2 family. Finally, we analyzed a computer series system dataset for illustration purposes, providing significant insights into the behavior of CKR uncertainty measures.

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