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Abstract:
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The Pareto distribution is widely used to model phenomena in many fields, including wildfire size and earthquake seismic moments. However, it has been found that the Pareto distribution often overestimates the frequency of the largest of these types of events. Instead, the tapered Pareto, which behaves like the Pareto but then gradually tapers off resulting in a shorter upper tail, often provides a better fit. Though the likelihood ratio test is optimal in assessing the goodness-of-fit between two models, this paper discusses a graphical test to distinguish between the Pareto and tapered Pareto distributions. Specifically, for distributions that seem to be better modeled by the tapered Pareto, the test will determine the point at which the self-similarity of the log survival function of the Pareto distribution ends. The properties of this graphical test will also be explored.
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