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Wykorzystanie entropii Shannona i jej uogólnień do badania rozkładu prawdopodobieństwa zmiennej losowej dyskretnej

100%
Wędrowska E.
Przegląd Statystyczny
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2010
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vol. 57
|
issue 4
39-53
EN
Everywhere where there is need for identification and measurement of indeterminacy of the distributions studied we can talk about entropy. The need to measure the degree of diversity occurs in studies on numerous systems, processes and phenomena, in particular in studies on socioeconomic phenomena. That is why in studies on those phenomena the measures or models defined on grounds of the information theory are used increasingly often. The paper presents categorization of notions and characteristics of the entropy of a discrete random variable. In addition to Shannon’s entropy, the Rényi’s and Tsallis entropies were applied for studies on the properties of distributions in case of probabilities of the random variables. The notion of entropy stemming from thermodynamics found application in many fields of sciences. Shannon’s entropy was defined on the grounds of the information theory, the Rényi’s entropy is the result of generalization of the Kolmogorov-Nagumo average while the Tsallis entropy is a certain function of Rényi’s entropy. The present paper unifies these approaches by presenting one general model of concentration measure that applies Rényi’s entropy.
PL
O entropii można mówić wszędzie tam, gdzie istnieje potrzeba rozpoznania i zmierzenia nieokreśloności badanych rozkładów zmiennych losowych. Potrzeba zmierzenia stopnia koncentracji występuje w badaniu wielu systemów, procesów czy zjawisk, w szczególności w badaniu zjawisk społeczno-ekonomicznych. Właśnie dlatego w badaniu tychże zjawisk coraz częściej wykorzystuje się miary zdefiniowane na gruncie teorii informacji. W artykule zaprezentowano pojęcia i własności entropii zmiennej losowej dyskretnej. Wykorzystano entropię Shannona wraz z jej uogólnieniami (entropią Rényiego i Tsallisa) do badania własności rozkładów prawdopodobieństw dyskretnych zmiennych losowych. Wskazano ponadto na liczne związki miar koncentracji dyskretnego rozkładu prawdopodobieństwa z entropią. W artykule zaproponowano miarę umożliwiającą ocenę stopnia koncentracji dyskretnego rozkładu prawdopodobieństwa będącą funkcją entropii Rényiego.
2
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THE USE OF CSISZÁR'S DIVERGENCE TO ASSESS DISSIMILARITIES OF INCOME DISTRIBUTIONS OF EU COUNTRIES

63%
Oczki J., Wędrowska E.
Metody Ilościowe w Badaniach Ekonomicznych
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2014
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vol. 15
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issue 2
167-176
EN
Income distributions can be described by measures of central tendency, dispersion, skewness, kurtosis or by indexes of polarization. In numerous studies, Gini coefficient and Lorenz curve have been used to investigate inequality of incomes. Income distributions can also be analysed in comparison to one another. In the article two measures belonging to Csiszár's divergence class have been used to identify the degree of differentiation of income distributions among the EU countries in 2005 and 2012. Similar and dissimilar countries with respect to distribution of income have been identified and the change of divergence of EU countries income distributions between 2005 and 2012 has been assessed. European Union Statistics on Income and Living Conditions (EU-SILC) dataset has been used.
3
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Income inequality of households in Poland: A subgroup decomposition of generalized entropy measures

63%
Muszyńska J., Wędrowska E.
Econometrics. Ekonometria. Advances in Applied Data Analytics
|
2018
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issue vol. 22 no. 4
43-64
EN
A formula of measures applied to assess the level of income inequality results from the intellectual basis on which this approach is founded. Our paper focuses on Generalized Entropy measures. The aim of our paper is two-fold. Firstly, it aims at presenting GE measures and discussing their properties, especially the property of additive decomposition. Secondly, the empirical aim is to assess the level of income inequality in Poland and to indicate its main determinants. In the study we use microdata obtained from EU-SILC that cover information about incomes received by individual household members in 2016. Five factors are chosen as the possible drivers of income inequality. The study proves the characteristics related to human capital are the most influential factors of income variability between households. The characteristics describing the composition of the household contribute to the overall level of inequality to a smaller extent.
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