On the parameters of Zenga distribution

Arcagni, Alberto; Porro, Francesco

doi:10.1007/s10260-012-0219-y

Cited by 12 publications

(13 citation statements)

References 13 publications

(10 reference statements)

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“…Similar results were obtained Fig. 11 The density distribution functions of the Zenga model for employees (on the left) and retired (on the right) using the A 1 , A 2 and A .′ 2 measures (Zenga et al 2010a;Arcagni and Porro 2013). It was shown that the Zenga distribution fits well with the data even with small and very small samples.…”

Section: Discussionsupporting

confidence: 74%

“…Zenga model has three parameters: is a scale parameter and it is equal to the expected value, and are shape parameters that inequality depends on. It means that this distribution controls the location and inequality separately so restrictions on the expected value and inequality measure can be imposed separately (Arcagni and Porro 2013). The estimated parameters of Zenga distribution can be found, through D'Addario's invariants method (Zenga et al 2010a;Arcagni 2011).…”

Section: Introductionmentioning

confidence: 99%

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Assessment of goodness of fit of income distribution in France and Germany based on the Zenga distribution

Ćwiek

Trzcińska

2022

Qual Quant

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The aim of this paper is to apply the Zenga distribution for equivalent disposable income from the last two waves of European Quality of Life Surveys for Germany and France (both for total society and selected socio-economic groups) and to assess the goodness of fit to empirical data. The Zenga distribution has not been used to describe the income distribution in these countries yet. The obtained parameters were assessed for fitting to empirical data using two measures—the Wasserstein-Kantorovich and the Wasserstein-Kantorovich standardized measure. The analysis of the results received allows for the conclusion that the Zenga distribution can fit the income distributions both for small as well as large values. It was also shown that the Zenga distribution fits the data well even with small and very small samples. The article uses a new measure to assess the fit of the distribution to empirical data, based on the Wasserstein-Kantorovich measure assessing the distance between the empirical and theoretical cumulative distribution function. The modification consisted in standardizing the Wasserstein-Kantorovich measure by dividing the field between distributors by the rectangle area, where length is maximum income and width is maximum value of the cumulative distribution function. The proposed measure is not sensitive to extreme values, often found in the analysis of income distribution, and can be applied even in very small samples.

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Section: Discussionsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Assessment of goodness of fit of income distribution in France and Germany based on the Zenga distribution

Ćwiek

Trzcińska

2022

Qual Quant

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“…The new density allows for a wider variety of shapes than the traditional three-parameter models of income distributions as for example the Dagum and Singh-Maddala distribution. The distribution depends on three parameters: in particular µ is a scale parameter, α in an inverse inequality indicator and it controls the tails of the distribution, while θ is a direct inequality indicator and it controls the distribution around the expected value µ (Arcagni, Porro, 2013).…”

Section: Zenga Distributionmentioning

confidence: 99%

Analysis of Household Income in Poland Based on the Zenga Distribution and Selected Income Inequality Measure

Trzcińska

2020

Folia Oeconomica Stetinensia

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Research background: A lot of research has been directed at describing empirical distributions by using a theoretical model. In the literature there are proposals for various types of mathematical functions. In 2010 Zenga proposed a new three-parameter model for economic size distribution which possesses interesting statistical properties which can be used to model income, wealth and financial variables.Purpose: The aim of this paper is to apply the Zenga model to income distributions in Poland by voivodeship.Research methodology: The basis for the calculations presented in the paper has been based on the individual data coming from a random sample obtained within a Household Budget Survey conducted by the central Statistical Office in the year 2014. The parameters estimates of the Zenga distribution were obtained by means of the D’Addario’s invariants methods, mainly with the Pietra index.Results: The results of the conducted approximations, presented in the paper confirmed the good consistency of the Zenga distribution with the empirical income distribution in Poland, both in total and for households.Novelty: The study contributed to the application of a new three-parameter income distribution model to describe income distributions in Poland.

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“…Theorem 8.4 (Arcagni & Porro, 2013). Assume X ∼ Zenga(µ X , α X , θ X ) and Y ∼ (Note that UCE F,u * (0) = E[u * (X)].)…”

Section: From Collective To Individual Referencesmentioning

confidence: 99%

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

Greselin

Zitikis

2015

SSRN Journal

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The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every Lorenz curve falls into. In this paper we argue that by appropriately choosing population-based references, called societal references, and distributions of personal positions, called gambles, which are random, we can meaningfully unify classical and contemporary indices of economic inequality, as well as various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.

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On the parameters of Zenga distribution

Cited by 12 publications

References 13 publications

Assessment of goodness of fit of income distribution in France and Germany based on the Zenga distribution

Assessment of goodness of fit of income distribution in France and Germany based on the Zenga distribution

Analysis of Household Income in Poland Based on the Zenga Distribution and Selected Income Inequality Measure

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

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