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Statistical Mirroring: A Good Alternative Estimator of Dispersion
Version 1
: Received: 21 November 2019 / Approved: 24 November 2019 / Online: 24 November 2019 (04:53:43 CET)
Version 2 : Received: 12 September 2021 / Approved: 13 September 2021 / Online: 13 September 2021 (13:26:35 CEST)
Version 2 : Received: 12 September 2021 / Approved: 13 September 2021 / Online: 13 September 2021 (13:26:35 CEST)
How to cite: Abdullahi, K. B. Statistical Mirroring: A Good Alternative Estimator of Dispersion . Preprints 2019, 2019110268. https://doi.org/10.20944/preprints201911.0268.v2 Abdullahi, K. B. Statistical Mirroring: A Good Alternative Estimator of Dispersion . Preprints 2019, 2019110268. https://doi.org/10.20944/preprints201911.0268.v2
Abstract
The statistical properties of a good estimator include robustness, unbiasedness, efficiency, and consistency. However, the commonly used estimators of dispersion have lack or are weak in one or more of these properties. In this paper, I proposed statistical mirroring as a good alternative estimator of dispersion around defined location estimates or points. In the main part of the paper, attention is restricted to Gaussian distribution and only estimators of dispersion around the mean that functionalize with all the observations of a dataset were considered at this time. The different estimators were compared with the proposed estimators in terms of alternativeness, scale and sample size robustness, outlier biasedness, and efficiency. Monte Carlo simulation was used to generate artificial datasets for application. The proposed estimators (of statistical meanic mirroring) turn out to be suitable alternative estimators of dispersion that is less biased (more resistant) to contaminations, robust to scale and sample size, and more efficient to a random distribution of variable than the standard deviation, variance, and coefficient of variation. However, statistical meanic mirroring is not suitable with a mean (of a normal distribution) close to zero, and on a scale below ratio level.
Keywords
isomorphic optinalysis; dispersion; statistical mirrors; estimators; statistical properties
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Kabir Bindawa Abdullahi
Commenter's Conflict of Interests: Author
1. Grammer checked.
2. Further details and clarifications on the concept of statistical mirroring.
2. Sections were re-structured and edited.