Measuring the stability of histogram appearance when the anchor position is changed

Although the histogram is the most widely used density estimator, it is well--known that the appearance of a constructed histogram for a given bin width can change markedly for different choices of anchor position. In this paper we construct a stability index $G$ that assesses the potential changes in the appearance of histograms for a given data set and bin width as the anchor position changes. If a particular bin width choice leads to an unstable appearance, the arbitrary choice of any one anchor position is dangerous, and a different bin width should be considered. The index is based on the statistical roughness of the histogram estimate. We show via Monte Carlo simulation that densities with more structure are more likely to lead to histograms with unstable appearance. In addition, ignoring the precision to which the data values are provided when choosing the bin width leads to instability. We provide several real data examples to illustrate the properties of $G$. Applications to other binned density estimators are also discussed.Bin width, frequency polygon, Gini index, linear binning, Lorenz curve, Monte Carlo simulation

Merelaniite, Mo4Pb4VSbS15, a New Molybdenum-Essential Member of the Cylindrite Group, from the Merelani Tanzanite Deposit, Lelatema Mountains, Manyara Region, Tanzania

This is an open access publicationThis is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0). The attached file is the published version of the article.© 2016 The Author(s). Published by Taylor & Francis. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/Licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The attached file is the published version of the article

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Fil: Simonoff, Alejandro. Universidad Nacional de La Plata. Facultad de Humanidades y Ciencias de la Educación. Instituto de Investigaciones en Humanidades y Ciencias Sociales (UNLP-CONICET); Argentina

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