Optimum Structural Probability Bounds for the Right-tail of the Paretian Law
The two-parameter Pareto density function [see PDF for equation] is widely used in applied statistics. For example, in reliability theory (1.1) represents the failure-time distribution of a "work-hardened" component whose.hazard function is inversely proportional to time. Because of its long right-tail, (1.1) is often a probability model for certain socioeconomic phenomena (e.g., distribution of city population sizes, distribution of personal incomes which exceed tax-exempt levels). One of the more recent characterizations of the Pareto distribution is due to Revankar, et. at. . They show that within the population of individuals that under-report their income for income tax purposes, the average under-reporting error for a given reported income is a linear function of the reported income if and only if the distribution of incomes in the population follows a Pareto distribution.