Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

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)

How to cite: Abdullahi, K.B. Statistical Mirroring: A Good Alternative Estimator of Dispersion . Preprints 2019, 2019110268. Abdullahi, K.B. Statistical Mirroring: A Good Alternative Estimator of Dispersion . Preprints 2019, 2019110268.


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.


isomorphic optinalysis; dispersion; statistical mirrors; estimators; statistical properties


Computer Science and Mathematics, Mathematics

Comments (1)

Comment 1
Received: 13 September 2021
Commenter: Kabir Bindawa Abdullahi
Commenter's Conflict of Interests: Author
Comment: The previous version of the manuscript has been revised for the following:
1. Grammer checked.
2. Further details and clarifications on the concept of statistical mirroring.
2. Sections were re-structured and edited. 
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