Data show that an increase in the Gini coefficient is associated with a falling bottom pB% income share and an increasing top pT% income share where, e.g. pB = 40 and pT = 1. This relationship, which we call the X inequality relationship, is pervasive in the sense that it is observed in many...

Given that the Lorenz curve is widely used for analyzing income distribution and inequality, this study introduces an alternative functional form for the Lorenz curve that is constructed based on the weighted average of the exponential function and the functional form implied by Pareto...

This Element presents the κ-generalized distribution, a statistical model tailored for the analysis of income distribution. Developed over years of collaborative, multidisciplinary research, it clarifies the statistical properties of the model, assesses its empirical validity and compares its...

There is considerable literature on matrix-variate gamma distributions, also known as Wishart distributions, which are driven by a shape parameter with values in the (Gindikin) set {i/2, i = 1, . . . , k−1}∪((k−1)/2, É). We provide an extension of this class to the case where the shape...

The generalized asymmetric Laplace (GAL) distribution, also known as the variance/mean-gamma model, is a popular flexible class of distributions that can account for peakedness, skewness, and heavier than normal tails, often observed in financial or other empirical data. We consider extensions...