Geometry of deviation measures for triangular distributions
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Published version
Date
2023-12-07
Authors
Wang, Yuhe
Pinsky, Eugene
Version
Published version
OA Version
Citation
Y. Wang, E. Pinsky. "Geometry of deviation measures for triangular distributions" Frontiers in Applied Mathematics and Statistics, Volume 9. https://doi.org/10.3389/fams.2023.1274787
Abstract
Triangular distributions are widely used in many applications with limited sample data, business simulations, and project management. As with other distributions, a standard way to measure deviations is to compute the standard deviation. However, the standard deviation is sensitive to outliers. In this paper, we consider and compare other deviation metrics, namely the mean absolute deviation from the mean, the median, and the quantile-based deviation. We show the simple geometric interpretations for these deviation measures and how to construct them using a compass and a straightedge. The explicit formula of mean absolute deviation from the median for triangular distribution is derived in this paper for the first time. It has a simple geometric interpretation. It is the least volatile and is always better than the standard or mean absolute deviation from the mean. Although greater than the quantile deviation, it is easier to compute with limited sample data. We present a new procedure to estimate the parameters of this distribution in terms of this deviation. This procedure is computationally simple and may be superior to other methods when dealing with limited sample data, as is often the case with triangle distributions.
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© 2023 Wang and Pinsky. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.