Characteristics Based Heuristics to Select a Logical Distribution between the Poisson-Gamma and the Poisson-Lognormal for Crash Data Modelling
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2019-11-01
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Abstract:Several studies have shown that the Poisson-lognormal (PLN) offers a better alternative compared to the Poisson-gamma (PG) when data are skewed while the PG is a more reliable option otherwise. However, it is not explicitly clear when the analyst needs to shift from the PG to the PLN – or vice versa. In addition, so far, the comparison has usually been accomplished using the goodness-of-fit statistics or statistical tests. Such metrics rarely give any intuitions into why a specific distribution or model is preferred over another. This paper addresses these topics by (1) designing characteristics-based heuristics to select a distribution between the PG and PLN, and (2) prioritizing the most important summary statistics to select a distribution between these two options. The results show that the kurtosis and percentage-of-zeros of data are among the most important summary statistics needed to distinguish between these two options.
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Content Notes:This is an open access article under the terms of the Creative Commons Attribution-Noncommercial-No Derivatives License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Citation: Shirazi, M., and D. Lord (2019) Characteristics Based Heuristics to Select a Logical Distribution between the Poisson-Gamma and the Poisson-Lognormal for Crash Data Modelling. Transportmetrica A: Transport Science, Vol 15, Issue 2, pp. 1791-1803. The digital object identifier for the published article is https://doi.org/10.1080/23249935.2019.1640313
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