binequality

Methods for model selection, model averaging, and calculating metrics, such as the Gini, Theil, Mean Log Deviation, etc, on binned income data where the topmost bin is right-censored. We provide both a non-parametric method, termed the bounded midpoint estimator (BME), which assigns cases to their bin midpoints; except for the censored bins, where cases are assigned to an income estimated by fitting a Pareto distribution. Because the usual Pareto estimate can be inaccurate or undefined, especially in small samples, we implement a bounded Pareto estimate that yields much better results. We also provide a parametric approach, which fits distributions from the generalized beta (GB) family. Because some GB distributions can have poor fit or undefined estimates, we fit 10 GB-family distributions and use multimodel inference to obtain definite estimates from the best-fitting distributions. We also provide binned income data from all United States of America school districts, counties, and states.

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