The Overlapping Coefficient: A Decision-Theoretic Study
References
- Alodat M.T., Al Fayez M., Eidous O.M. (2022): On the asymptotic distribution of Matusita’s overlapping measure. Communications in Statistics – Theory and Methods 51(20): 6963–6977.
- Berger J.O. (1985): Statistical decision theory and Bayesian analysis (2nd ed.). Springer-Verlag.
- Bishop C.M. (2006): Pattern recognition and machine learning. Springer.
- Diakonikolas I., Kane D.M. (2023): Algorithmic high-dimensional robust statistics. Cambridge University Press.
- Duda R.O., Hart P.E., Stork D.G. (2001): Pattern classification (2nd ed.). John Wiley & Sons.
- Eidous O.M., Abu Al-Hayja’a M.M. (2023a): Estimation of overlapping measures using numerical approximations: Weibull distributions. Jordan Journal of Mathematics and Statistics (JJMS) 16(4): 741–761.
- Eidous O.M., Abu Al-Hayja’a M.M. (2023b): Numerical integration approximations to estimate the Weitzman overlapping measure: Weibull distributions. Yugoslav Journal of Operations Research 33(4): 699–712.
- Eidous O.M., Al-Rawwash M.Y. (2025): Approximations for standard normal distribution function and its invertible. Journal of Algorithms & Computational Technology 19, 1–5. doi:10.1177/17483026251322100
- Eidous O.M., Alsheyyab M.M. (2025): Generalization of the overlapping coefficient for k ≥ 2 normal distributions. Mathematical Modelling of Natural Phenomena 20, Article 9. https://doi.org/10.1051/mmnp/2025008
- Eidous O.M., Alshorman A.J.A. (2023): Estimating the Weitzman overlapping coefficient using integral approximation method in the case of normal distributions. Advances in Transdisciplinary Engineering 42: 1011–1020.
- Eidous O.M., Al-Talafha S.A. (2022): Kernel method for overlapping coefficients estimation. Communications in Statistics – Simulation and Computation 51(9): 5139–5156.
- Eidous O.M., Ananbeh E. (2022): Approximations for cumulative distribution function of standard normal. Journal of Statistics and Management Systems 25(3): 541–547.
- Eidous O.M., Ananbeh E.A. (2024): Kernel method for estimating overlapping coefficient using numerical integration methods. Applied Mathematics and Computation 462, 128339.
- Eidous O.M., Ananbeh E.A. (2025): Kernel method for estimating Matusita overlapping coefficient using numerical approximations. Annals of Data Science 12(4): 1265–1283.
- Eidous O.M., Daradkeh S.K. (2024): On inference of Weitzman overlapping coefficient Δ(X, Y) in the case of two normal distributions. International Journal of Theoretical and Applied Mathematics 10(2): 14–22.
- Eidous O., Maqableh H. (2023): Estimation of Matusita overlapping coefficient ρ for two Weibull distributions. Journal of Statistics and Computer Science 2(1): 1–16.
- Eidous O., Maqableh H. (2024): Estimation of Morisita overlapping measure λ for two Weibull distributions. World Journal of Mathematics and Statistics 3(2): 13–21.
- Hastie T., Tibshirani R., Friedman J. (2009): The elements of statistical learning: data mining, inference, and prediction (2nd ed.). Springer.
- Inman H.F., Bradley E.L. (1989): The overlapping coefficient as a measure of agreement between probability distributions and point estimation of the overlap of two normal densities. Communications in Statistics – Theory and Methods 18(10): 3851–3874.
- Li C., Liu K., Liu S. (2025): A survey of loss functions in deep learning. Mathematics 13(15): 2417.
- Maqableh H.Y., Eidous O.M. (2024): On inference of Weitzman overlapping coefficient in two Weibull distributions. Journal of Health Statistics Reports 3(3): 1–6.
- Martínez-Camblor P. (2023): About the use of the overlap coefficient in the binary classification context. Communications in Statistics – Theory and Methods 52(19): 6767–6777.
- Memon S.A., Ahmad I., Shoaibullah (2025): Mathematical analysis of loss functions in classification and regression. Physical Education Health and Social Sciences, 3(2): 96–103.
- Pastore M., Calcagnì A. (2019): Measuring distribution similarities between samples: A distribution-free overlapping index. Frontiers in Psychology 10, 589.
- Wald A. (1950): Statistical decision functions. New York: John Wiley & Sons.
- Wheat L., Mohrenschildt M.V., Habibi S. (2025): Bayes error rate estimation in difficult situations. arXiv preprint arXiv:2506.03159.
- Weitzman M.S. (1970): Measures of overlap of income distributions of white and negro families in the United States (Technical Paper No. 22). US Bureau of the Census.
DOI: https://doi.org/10.2478/bile-2026-0011 | Journal eISSN: 2199-577X (formerly 1896-3811) | Journal ISSN: 1896-3811
Language: English
Published on: Nov 10, 2026
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Keywords:
Related subjects:
© 2026 Omar M. Eidous, Bashar O. Edous, Mohammad O. Edous, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.