Statistical Size Distributions in Economics and Actuarial Sciences

“…For the subset of analyses in which inequality is represented by the general inequality parameter in continuous univariate two-parameter distributions, we use three variates whose properties are well-known and make them appealing models for distributions of wages, income, wealth, and other economic variables -the lognormal, Pareto, and power-function Balakrishnan, 1994, 1995;Kleiber and Kotz, 2003). The lognormal and the power-function have their origin at zero and thus have no safety net, while the Pareto, in contrast, does.…”

Section: Building Blocks: Probability Distributionsmentioning

confidence: 99%

(In)Equality and (In)Justice

Jasso

2016

Civitas

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Exceto onde especificado diferentemente, a matéria publicada neste periódico é licenciada sob forma de uma licença Creative Commons -Atribuição 4. Guillermina Jasso* Abstract: Understanding the connection between inequality and justice is important because justice is classically regarded as the first line of defense against self-interest and inequality. Absent a strong and clear link between inequality and justice, the sense of justice would not awaken to exert its moral suasion, no matter how great the inequality or how fast its increase. We obtain exact links between economic inequality and three parameters of the justice evaluation distribution -the mean, median, and varianceacross a comprehensive set of inequality measures and a substantial starter set of just reward scenarios. This work shows that there is no general necessary connection between inequality and justice. There is, however, a striking pattern in some situations: as economic inequality increases, the average of the justice evaluations moves deeper into the territory of unjust underreward, and the distribution stretches outward, increasing the gulf between underrewarded and overrewarded and hollowing out the middle class. Resumo: Compreender a conexão entre desigualdade e justiça é importante porque a justiça é classicamente considerado como a primeira linha de defesa contra o autointeresse e a desigualdade. Na ausência de uma ligação forte e clara entre desigualdade e justiça, o senso de justiça não iria despertar para exercer a sua persuasão moral, não importa quão grande a desigualdade ou o quão rápido o seu crescimento. Neste trabalho analisamos as ligações entre desigualdade econômica e três parâmetros da distribuição de avaliação de justiça -média, mediana e variância -através de um conjunto abrangente de medidas de desigualdade e um conjunto inicial substantivo de cenários de justa recompensa. Este trabalho mostra que não há nenhuma conexão geral necessária entre desigualdade e justiça. Há, no entanto, um padrão marcante em algumas situações: com o aumento da desigualdade econômica, a média das avaliações de justiça se move mais profundamente no território de injustamente sub-recompensado, e a distribuição se estende para fora, aumentando o abismo entre sub-recompensado e super-recompensado, esvaziando as categorias intermediárias.Palavras-chave: Desigualdade. Justiça. Equidade. Distribuições de probabilidade. Medidas de desigualdade e de justiça e equidade.

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“…As x → 0, the left-hand side of (16) clearly converges to ρ(0); the Lebesgue theorem on dominated convergence implies that the right-hand side of equation (16) converges to…”

Section: Theoremmentioning

confidence: 99%

On stable Pareto laws in a hierarchical model of economy

Chebotarev¹

2007

Physica A: Statistical Mechanics and its Applications

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This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities move from senior to junior partners and money moves in the opposite direction. The priceinvariance of transactions means that the probability of a pairwise interaction is a function of the ratio of incomes, which is independent of the price scale or absolute income level. These two features characterize the hierarchical model. The income distribution in this class of models is a well-defined double-Pareto function, which possesses Pareto tails for the upper and lower incomes. For gross and net upper incomes, the model predicts definite values of the Pareto exponents, a gross and a net , which are stable with respect to quantitative variation of the pair-interaction. The Pareto exponents are also stable with respect to the choice of a demand function within two classes of status-dependent behavior of agents: linear demand (a gross = 1, a net = 2) and unlimited slowly varying demand (a gross = a net = 1). For the sigmoidal demand that describes limited returns, a gross = a net = 1 + α, with some α > 0 satisfying a transcendental equation. The low-income distribution may be singular or vanishing in the neighborhood of the minimal income; in any case, it is L 1 -integrable and its Pareto exponent is given explicitly.The theory used in the present study is based on a simple balance equation and new results from multiplicative Markov chains and exponential moments of random geometric progressions.

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Statistical Size Distributions in Economics and Actuarial Sciences

Cited by 916 publications

References 355 publications

A non-parametric structural hybrid modeling approach for electricity prices

A non-parametric structural hybrid modeling approach for electricity prices

(In)Equality and (In)Justice

On stable Pareto laws in a hierarchical model of economy

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