We consider concepts and models that are useful for measuring how strongly the distribution of a positive response Y is concentrated near a value with a focus on how concentration varies as a function of covariates. We combine ideas from statistics, economics and reliability theory. Lorenz...

The Gini index is often used to measure the income inequality presented inside a specified group of individuals and sometimes also for evaluating the “poverty” degree of this population. In this article we show that Gini’s index is not always so adequate to measure the poverty level of an...

Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss...

En este artículo se proporciona una herramienta que permite estudiar las distribuciones de renta en una población a lo largo del tiempo, sin importar que los datos se distribuyan de forma irregular. Incluso, se posibilita la aproximación de curvas de Lorenz en instantes en los que no se...

An ideal state of development, when viewed with fantasy, is nothing but a state or condition where light touches everybody without refraction. The diagonal line of the Lorenz Curve Framework represents such an ideal condition. In the presence of inequality, however, it deviates or refracts from...

This article provides a tool to study over time the distributions of income in a population, regardless the irregular distribution of data. We even approach Lorenz curves at the times when we lack the required data. Finally we apply the present technique to a European country where inequalities...

This paper explores an elemental connection between call options–the most commonly tradable financial derivatives, implied volatility term structures–critical “market information” emanating from call-option prices, and the Pietra index–a quantitative economic measure of societal...

We consider concepts and models that are useful for measuring how strongly the distribution of a positive response Y is concentrated near a value with a focus on how concentration varies as a function of covariates. We combine ideas from statistics, economics and reliability theory. Lorenz...

This paper introduces in statistics the notion of the barycenter of the distribution of a non-negative random variable Y with a positive finite mean μY and the quantile function Q(x). The barycenter is denoted by μX and defined as the expected value of the random variable X having the...

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...