We show how a collection of results in the literature on the empirical estimation of welfare indicators from sample data can be unified. We also demonstrate how some of these ideas can be extended to empirically important cases where the data have been trimmed or censored.

This article analyzes the mathematical connections between two kinds of inequality: inequality between persons (e.g., income inequality) and inequality between subgroups (e.g., racial inequality). The authors define a general inequality parameter in two-parameter continuous distributions. This...

The well-known discrete theory of conjugate partitions, Ferrers graphs and Durfee squares is interpreted in informetrics. It is shown that partitions and their conjugates have the same h-index, a fact that is not true for the g- and R-index. A modification of Ferrers graph is presented, yielding...

While various authors have appealed to Dalton's Principle of Transfers, the Lorenz curve, and the Gini Coefficient to assess disproportionality in proportional representation systems, some additional clarifications are warranted with regard to these concepts and their proper application to the...

Amato (1968) proposed using the length of the Lorenz curve as an index of inequality. The index has been little used, perhaps because of the perceived difficulty in analytically evaluating the value of the index in specific situations. A simple representation of the index as an expectation of a...

We describe several simulation algorithms that yield random probability distributions with given values of risk measures. In case of vanilla risk measures, the algorithms involve combining and transforming random cumulative distribution functions or random Lorenz curves obtained by simulating...

We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a...

Recently, a lot of attention is given to income variations occurring at the top of the income distribution. “What happens to the top 1%?” is a question of crucial importance on the political level (Occupy Wall Street Movement) as well as on income inequality measurement level. Despite this...

Over the last 100 years, a large number of distributions has been proposed for the modeling of size phenomena, notably the size distribution of personal incomes. The most widely known of these models are the Pareto, log-normal, generalized log-normal, generalized Gamma, generalized Beta of the...

Poverty and inequality are often estimated from grouped data as complete household surveys are neither always available to researchers nor easy to analyze. In this study we assess the performance of functional forms proposed by Kakwani (1980a) and Villasenor and Arnold(1989) to estimate the...