A series of papers by Hickey (1982, 1983, 1984) presents a stochastic ordering based on randomness. This paper extends the results by introducing a novel methodology to derive models that preserve stochastic ordering based on randomness. We achieve this by presenting a new family of pseudometric spaces based on a majorization property. This class of pseudometrics provides a new methodology for deriving the randomness measure of a random variable. Using this, the paper introduces the Gini randomness measure and states its essential properties. We demonstrate that the proposed measure has certain advantages over entropy measures. The measure satisfies the value validity property, provides an adequate extension to continuous random variables, and is often more appropriate (based on sensitivity) than entropy in various scenarios.

Comparative studies of inequality based on archaeological data rely on universal notions of status or prestige that are not always meaningful across diverse cultural contexts. Here, the authors evaluate three broadly contemporaneous urban communities (Marothodi, Molokwane and Kaditshwene) in the southern African interior in the eighteenth and nineteenth centuries AD. The study combines a statistical measure of inequality, the Gini coefficient, with insights from the rich ethnohistorical archives of African knowledge systems. The results suggest markedly different levels of inequality, but contextualisation points to divergent social strategies for settlement organisation and for managing sociopolitical insecurity. The findings raise important questions about cross-cultural indices of social inequality.

During the Late Classic period (a.d. 550–900), ancient Maya settlement spread throughout western Belize, including the Vaca Plateau, a rugged karstic region with high densities of ritually utilized cave systems. Within the past decade, archaeologists have increasingly drawn on LiDAR technology to document the extent of such settlement at local and regional scales. Combined with traditional pedestrian survey, we have begun to amass substantial data on variation within household groups, disparities which may indicate inequality within these communities. Here, we use settlement data generated from the Las Cuevas region to quantify residential variation through Gini coefficients and Lorenz curves. Special attention is given to areal and volumetric deviation of identified households within three samples: (1) the complete 95.25 km2 study area; (2) a 12.25 km2 zone of higher population between the primary centers of Las Cuevas and Monkey Tail; and (3) households situated within 500 m of ritually utilized caves within the study area. Results indicate some degree of variation within household area and volume for all samples, suggestive of unequal access to labor within the region. This research adds to the growing database of Gini-based analyses to improve our understanding of wealth differentials within pre-modern populations throughout the Lowlands.

This article reviews the rationale for and various approaches used by economists to incorporate distributional consequences of projects or policies into benefit-cost analyses. Approaches reviewed include distributional weights and metrics based on the Lorenz curve. Analysis of distributional issues in partial equilibrium and general equilibrium settings are briefly reviewed. We present an empirical demonstration of how the contingent valuation method (CVM) and hedonic property methods (HPM) can be used to quantify how non-market environmental benefits are distributed by income and ethnicity. Using CVM, the distribution of non-market benefits can be cross-tabbed with respondent demographics, so that a variety of “distributions” of benefits by relevant demographic groups can be calculated. Using the HPM, the analyst can statistically test to see if the implicit price gradient varies with differences in income and ethnicity. In our empirical example, we find that ethnicity and income interaction terms on the implicit price gradient are statistically significant suggesting differential effects of National Forest fire suppression policies on Hispanics and low income households.

This paper examines the role of the life cycle in impacting the distribution of a combined income and wealth measure using data from the 2001 and 2006 Agricultural Resource Management Survey. Such an assessment is made using both graphical representation of the distribution of the well-being measure along with utilization of the social welfare decomposition procedure. Results show a mild yet statistically insignificant improvement in the distribution of the economic measure over the five-year period. Contribution to social welfare is found highest among the cohort where the age of the head of household is between 45 and 54 years. Targeted programs are found to enhance social welfare if they are aimed towards cohorts where the age of the head of household is younger than 35 years or where the age of the head of household is in the 35-to-44 age group, depending on whether the analysis is based on a perfarm household or on a per-capita basis.

The method of computing wealth shares accruing to lowest and highest quintiles, along with the concepts of the Lorenz curve and the Gini coefficient, are used in conjunction with data from the 1996 and 1999 Agricultural Resource Management Study (ARMS) survey to measure the distribution of wealth among U.S. farm operator households. Findings show that the distribution of wealth in 1996 was slightly more concentrated than in 1999, with the farm wealth component contributing significantly more toward measured concentration in both years than the nonfarm wealth component. The robustness of the findings under varied value judgments concerning society's level of aversion to wealth concentration is also examined.

In this paper we study asymptotic behavior of convexrearrangements of Lévy processes. In particular weobtain Glivenko-Cantelli-type strong limit theorems for the convexifications when the corresponding Lévy measureis regularly varying at + with exponent α ∈ (1,2).

By using Chibisov-O'Reilly type theorems for uniform empirical and quantile processes based on stationary observations, we establish a weak approximation theory for empirical Lorenz curves and their inverses used in economics. In particular, we obtain weak approximations for empirical Lorenz curves and their inverses also under the assumptions of mixing dependence, often used structures of dependence for observations.