The Theil indices (Theil, ) are widely used measures for studying the degree of concentration and inequality in size income distributions. Their property decomposability makes these especially useful applied economic analysis. This paper is a synthetic review most important popular parametric Extensions to higher dimensions sketched.

<title>Abstract</title> This paper presents the first estimates of global and regional income polarizationtrends from 1960 to 2020. Our analysis relies on bipolarization indices a polarizationmeasure (DER) that accounts for multiple poles in distribution.We employ both relative absolute indexes, introducing parametrization ofthe DER index is simultaneously scale- translation-invariant. findingsshow while polarization has unambiguously declined since 1980s,absolute continues rise, except at...

The class of beta-generated distributions (Commun. Stat. Theory Methods 31:497–512, 2002; TEST 13:1–43, 2004) has received a lot attention in the last years. In this paper, three new classes bivariate are proposed. These constructed using different definitions with classical beta marginals and covariance structures. We work proposed (J. Educ. 7:271–294, 1982; Metrika 54:215–231, 2001; Probability Lett. 62:407–412, 2003) for first proposal, (Stat. Appl. 18: 465–481, 2009) second proposal...

Abstract The distribution of the sum dependent risks is a crucial aspect in actuarial sciences, risk management and many branches applied probability. In this paper, we obtain analytic expressions for probability density function (pdf) cumulative (cdf) aggregated risks, modelled according to mixture exponential distributions. We first review properties multivariate distributions, then analytical formulation pdf cdf distribution. study detail some specific families with Pareto (Sarabia et al....

In this paper, the class of Lamé Lorenz curves is studied. This family has advantage modeling inequality with a single parameter. The double motivation: it can be obtained from an economic model and simple transformations classical curves. underlying cumulative distribution functions have closed form, correspond to Singh–Maddala Dagum distributions, which are well known in literature. order studied several polarization measures obtained, including Gini, Donaldson–Weymark–Kakwani, Pietra,...

Despite the growing interest in global inequality, assessing inequality trends is a major challenge because individual data on income or consumption not often available. Nevertheless, periodic release of certain summary statistics distribution has become increasingly common. Hence, grouped form shares have been conventionally used to construct based lower bound approximations measures. This approach introduces two potential sources measurement error: first, these estimates are constructed...

Abstract Grouped data in the form of income shares have conventionally been used to estimate inequality due lack individual records. We present a systematic evaluation performance parametric distributions and non-parametric techniques economic using more than 3300 sets. also provide guidance on choice between these two approaches their estimation, for which we develop GB2group R package. Our results indicate that even simplest models reliable estimates measures. The approach, however, fails...

Abstract Monitoring health is key for identifying priorities in public planning and improving healthcare services. Life expectancy has conventionally been regarded as a valuable indicator to compare the status of different populations. However, this measure simply mean distribution length life and, such, neglects individual disparities outcomes. In paper, we use tables from UN World Population Prospects develop most comprehensive dataset lifespan inequality polarization 258 countries areas...

The general beta of the second kind distribution (GB2) is a flexible which includes several relevant parametric families distributions. This has important applications in earnings and income distributions, finance insurance. In this paper, multivariate classes GB2 are proposed. different versions based on two simple univariate representations distribution. first type distributions constructed from stochastic dependent defined terms gamma random variables. Using representation beginning by...

Abstract A strand of the political economy literature emphasizes effect income inequality on growth and poverty, which materialises through redistribution. The theoretical expectation postulated by standard economic theory is that high would lead to higher redistribution via collective action median voter. empirical testing voter theorem has been conducted in context industrialised economies. In this article, we examine hypothesis with specific reference SSA, a region characterised levels...

In this paper we study global inequality in well-being taking as a reference the Human Development Index. One of main changes applied to indicator was substitution arithmetic mean for geometric construction index, thus assuming different grades between dimensions. order determine impact aggregation formula distribution HDI, propose use multidimensional generalized entropy measures, which allow us evolution based on schemes. The results obtained suggest reduction human development over period...