The Pareto distribution is a simple model for nonnegative data with a power law probability tail. In many practical applications, there is a natural upper bound that truncates the probability tail. This article derives estimators for the truncated Pareto distribution, investigates their properties, and illustrates a way to check for fit. These methods are illustrated with applications from finance, hydrology, and atmospheric science.
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Aban et al. (2006) studied this question.