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Kernel method for estimating overlapping coefficient using numerical integration methods

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  • Eidous, Omar M.
  • Ananbeh, Enas A.

Abstract

In this paper, we proposed three nonparametric kernel estimators for the overlapping Weitzman measure Δ. Due to the difficulty of finding a general expression for Δ when the nonparametric kernel method is adopted, we suggest using the numerical integration method as the first stage of our estimation process. In particular, three numerical integration rules are considered, which are known as, trapezoidal and Simpson rules. The statistical properties of the resulting estimators are studied and investigated by using the simulation technique and their performances are also compared with some existing nonparametric kernel estimators developed by Eidous and Al-Talafhah (2020). The numerical results demonstrated the superiority and usefulness of the proposed technique over that suggested by Eidous and Al-Talafhah in estimating the overlapping measure Δ.

Suggested Citation

  • Eidous, Omar M. & Ananbeh, Enas A., 2024. "Kernel method for estimating overlapping coefficient using numerical integration methods," Applied Mathematics and Computation, Elsevier, vol. 462(C).
    • Handle: RePEc:eee:apmaco:v:462:y:2024:i:c:s0096300323005088
    DOI: 10.1016/j.amc.2023.128339
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    References listed on IDEAS

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    1. Wang, Dan & Tian, Lili, 2017. "Parametric methods for confidence interval estimation of overlap coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 12-26.
    2. Hani M. Samawi & Amal Helu & Robert Vogel, 2011. "A nonparametric test of symmetry based on the overlapping coefficient," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 885-898, February.
    3. Schmid, Friedrich & Schmidt, Axel, 2006. "Nonparametric estimation of the coefficient of overlapping--theory and empirical application," Computational Statistics & Data Analysis, Elsevier, vol. 50(6), pages 1583-1596, March.
    4. Hamza Dhaker & Papa Ngom & Boubakari Ibrahimouf & Malick Mbodj, 2019. "Overlap Coefficients Based on Kullback-Leibler of Two Normal Densities: Equal Means Case," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(2), pages 114-124, April.
    5. Mulekar, Madhuri S. & Mishra, Satya N., 2000. "Confidence interval estimation of overlap: equal means case," Computational Statistics & Data Analysis, Elsevier, vol. 34(2), pages 121-137, August.
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