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A relative-rank measure for the rank transformation

Author

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  • Hussain, Abid
  • Drekic, Steve
  • Cheema, Salman A.

Abstract

This research introduces a new ranking scheme capable of ordering competing units in a more continual manner. The classic ranks are functionalized by incorporating data range and quantile coverage simultaneously in the proposed formula. This dual use of additional information is found to enhance the sensitivity of the devised scheme towards offering more competent weights of competing observations. Some key mathematical properties of the proposed approach are highlighted. In particular, the capability of the devised approach in offering unambiguous preferences is established. Finally, the performance of the proposed measure is investigated under a set of diverse parametric settings involving different stochastic formulations, sample sizes, and degrees of correlation.

Suggested Citation

  • Hussain, Abid & Drekic, Steve & Cheema, Salman A., 2024. "A relative-rank measure for the rank transformation," Statistics & Probability Letters, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:stapro:v:204:y:2024:i:c:s0167715223001566
    DOI: 10.1016/j.spl.2023.109932
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    References listed on IDEAS

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    1. C. Acuña-Soto & V. Liern & B. Pérez-Gladish, 2021. "Normalization in TOPSIS-based approaches with data of different nature: application to the ranking of mathematical videos," Annals of Operations Research, Springer, vol. 296(1), pages 541-569, January.
    2. Germinal Cocho & Jorge Flores & Carlos Gershenson & Carlos Pineda & Sergio Sánchez, 2015. "Rank Diversity of Languages: Generic Behavior in Computational Linguistics," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-12, April.
    3. Gormley, Isobel Claire & Murphy, Thomas Brendan, 2008. "Exploring Voting Blocs Within the Irish Electorate," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1014-1027.
    4. Kanupriya Adlakha & Sanjeev Sharma, 2020. "Brand Positioning Using Multidimensional Scaling Technique: An Application to Herbal Healthcare Brands in Indian Market," Vision, , vol. 24(3), pages 345-355, September.
    5. Gerardo Iñiguez & Carlos Pineda & Carlos Gershenson & Albert-László Barabási, 2022. "Dynamics of ranking," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
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