From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

Greselin, Francesca; Zitikis, Ričardas

doi:10.3390/econometrics6010004

Cited by 18 publications

(16 citation statements)

References 104 publications

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“…Inequality was measured with the Gini's concentration coefficient (G) in its traditional formulation [60]. Since the exact distribution of incomes is not known.…”

Section: Data Set and Methodsmentioning

confidence: 99%

The Spatial Dimension of Income Inequality: An Analysis at Municipal Level

Mastronardi

Cavallo

2020

Sustainability

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This paper focuses on the analysis on income inequality in Italy at the municipal level of the areas defined by the National Strategy for Inner Areas. We discuss an analysis of the economic and spatial dynamics of the phenomenon through the construction of the Gini's coefficient and the estimation of the regression model for the evaluation of the determinants of inequality. We highlight the influence of the spatial dimension on income inequality in Italy. Inequality appears to be greater in densely populated urban centers with a strong incidence of tertiary activities and young population. Conversely, in the inner areas, the distribution of income is more balanced due probably to the weakness of the social and economic structure that determines low levels of income and job opportunities mainly in the agricultural sector. Sustainability 2020, 12, 1622 2 of 18 Sustainability 2020, 12, x FOR PEER REVIEW 11 of 18 355 Figure 2. Map of significance of the LM index for the values of the Gini coefficient. Source: own 356 elaboration. 357Consequently, the analyses are based on a classic linear regression model. Table 4 shows its main 358 results. The histogram of the residuals is showed Figure 3. 359A first element of reflection is that the model explains 60% of the observed variability, 360 confirming the strong territorial characterization of inequality in Italy. A second consideration is that, 361 except L, all the selected variables are quite significant. In detail, the t ratio between coefficients and 362 standard errors reports the relative variation of Gini coefficent, associated with a unitary variation of 363 the explanatory variables. The last columns on the right show the p values and the relative 364 significance under the hypothesis of robust standard errors with respect to heteroskedasticity (i.e., in 365 the presence of a nonconstant variance between the residuals or discrepancies between observed and 366 estimated values of the dependent variable, a possible cause of distorted estimations of the model 367 parameters). 369Lisa significance map High-High (928) High-Low (39) Low-High (27) Low-Low (809)

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“…Inequality was measured with the Gini's concentration coefficient (G) in its traditional formulation [60]. Since the exact distribution of incomes is not known.…”

Section: Data Set and Methodsmentioning

confidence: 99%

The Spatial Dimension of Income Inequality: An Analysis at Municipal Level

Mastronardi

Cavallo

2020

Sustainability

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“…These curves finds applications in many areas, such as economics, reliability, medicine and insurance. A nice survey in this regard can be found in [26].…”

Section: Incomplete Momentsmentioning

confidence: 99%

Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications

Aldahlan¹,

Jamal²,

Chesneau³

et al. 2020

PLoS ONE

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In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies.. .). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.

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“…Remark 3 Some other generalizations of the distortion premium were studied in Greselin and Zitikis 2018 [10], where they consider a class of functionalŝ…”

Section: Theorem 2 Any Distortion Premium Can Be Written Asmentioning

confidence: 99%

The distortion principle for insurance pricing: properties, identification and robustness

Escobar

Pflug

2018

Ann Oper Res

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Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness w.r.t. ambiguity of the loss distribution. Ambiguity is measured by the Wasserstein distance. We study variances of distances for probability models and identify some worst case distributions. In addition to the direct problem we also investigate the inverse problem, that is how to identify the distortion density on the basis of observations of insurance premia.

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From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

Cited by 18 publications

References 104 publications

The Spatial Dimension of Income Inequality: An Analysis at Municipal Level

The Spatial Dimension of Income Inequality: An Analysis at Municipal Level

Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications

The distortion principle for insurance pricing: properties, identification and robustness

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