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Highest density regions refer to level sets containing points of relatively high density. Their estimation from a random sample, generated from the underlying density, allows to determine the clusters of the corresponding distribution. This task can be accomplished considering different nonparametric perspectives. From a practical point of view, reconstructing highest density regions can be interpreted as a way of determining hot-spots, a crucial task for understanding COVID-19 space-time evolution. In this work, we compare the behaviour of classical plug-in methods and a recently proposed hybrid algorithm for highest density regions estimation through an extensive simulation study. Both methodologies are applied to analyse a real data set about COVID-19 cases in the United States. [ABSTRACT FROM AUTHOR]

After a hundred years of contributions, the debate about how to measure inequality is still open. We provide a brief review of the literature, showing that inequality has been assessed through a relative approach, from Gini's pioneering article [Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti 73 (1914), no. 2, 1203-1248]. Analyzing historical census data for Flint and other American cities, we observe how mean values of income in population subgroups capture the shape of the distributions of income and their comparisons state the overall situation of inequality. Namely, we adopted the approach introduced in [Statistica & Applicazioni 5 (2007), no. 1, 3-27] to assess inequality. Our first findings show that prosperity is distributed unevenly across America's metropolitan areas. More interestingly, unbalanced wealth can be related to other concomitant facts [The New Geography of Jobs, Houghton Mifflin Harcourt, New York, 2012], such as population growth, income growth, unemployment rates and women participation to the labor force. Gaps between more and less educated areas were modest 40 years ago, but they have become quite large nowadays [Cities and skills, technical report, National Bureau of Economic Research, 1994]. [ABSTRACT FROM AUTHOR]