Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Fundamentally Good Alternative to Normal Distribution

Version 1 : Received: 15 September 2022 / Approved: 19 September 2022 / Online: 19 September 2022 (02:06:09 CEST)

How to cite: Abdullahi, K.B. Fundamentally Good Alternative to Normal Distribution. Preprints 2022, 2022090252. https://doi.org/10.20944/preprints202209.0252.v1 Abdullahi, K.B. Fundamentally Good Alternative to Normal Distribution. Preprints 2022, 2022090252. https://doi.org/10.20944/preprints202209.0252.v1

Abstract

Location-and-scale transformation of a random variable underpins normal distribution, but it is however fundamentally incorrect for scale estimation such as relative dispersion. In this paper, a parametrized alternative to a normal distribution, called scaloc-normal distribution, is proposed that efficiently works and is fundamentally correct with absolute and relative dispersion estimators. The Monte Carlos simulation experiment was used to generate a total of 600,000 artificial datasets in 600 different simulation scenarios from loc-normal (normal) and scaloc-normal distributions. The absolute and relative dispersion were estimated and compared from the two distributions. The results show that scaloc-normal distribution is a good parametrized alternative to loc-normal distribution, fundamentally correct and efficient with both standard deviation and coefficient of variation. The key statistical advancement from loc-normal to scaloc-normal distribution is its fundamental correctness (i.e., scale-invariant property) with an efficient relative estimator of dispersion (i.e., coefficient of variation). Parametrically, the loc-normal and scaloc-normal distributions are very different, but both have linear transformations.

Keywords

alternative parameterization; normal distribution; dispersion estimators; location-invariance; scale-invariance; scale-and-location-invariance

Subject

Computer Science and Mathematics, Probability and Statistics

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