### Journals Information

Mathematics and Statistics Vol. 8(6), pp. 637 - 644
DOI: 10.13189/ms.2020.080603
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## Construction of Lorenz Curves Based on Empirical Distribution Laws of Economic Indicators

Aleksandr Bochkov 1,*, Dmitrii Pervukhin 2, Aleksandr Grafov 3, Veronika Nikitina 4
1 Department of Information and Computing Systems, Faculty of Automation and Intelligent Technologies, Emperor Alexander I St. Petersburg State Transport University, St. Petersburg, Russia
2 Department of System Analysis and Management, Faculty of Economics, St. Petersburg Mining University, St. Petersburg, Russia
3 Department of Economic Security, Faculty of Business, Customs and Economic Security, St. Petersburg State University of Economics, St. Petersburg, Russia
4 Department of Neurology and Manual Therapy, Faculty of Postgraduate Studies, Academician I.P. Pavlov First St. Petersburg State Medical University, St. Petersburg, Russia

ABSTRACT

The quality of construction of Lorenz curves depends on the features of the information used. As a rule, information is represented by a sample of values of the studied indicator, which is checked for unevenness. Economic indicators of income and cost, and features of their samples are considered. The feature of the cost economic indicator associated with the presence in the sample of its values of the clot is highlighted (the concentration of values on a small segment of the entire range of sample). It is shown that the established order of constructing empirical laws based on such samples does not give the desired effect when constructing Lorenz curves due to the loss of information content of the sample in the places of the clot. The purpose of this article is to improve the quality of the Lorenz curve by increasing the information content of the sample with a clot by applying the clustering procedure when constructing an empirical law. A step-by-step clustering procedure is proposed for dividing the entire range of sample into intervals to construct an empirical distribution law, which is an element of the novelty of this study. A specific example shows how to improve the quality of building a Lorenz curve using this procedure. In addition, it is shown that Lorenz curves for economic indicators can be constructed directly on the basis of the empirical distribution law and at the same time take into account its features.

KEYWORDS
Lorenz Curve, Empirical Distribution Law, Clustering, Histogram, Economic Indicators, Information Content of the Sample

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Aleksandr Bochkov , Dmitrii Pervukhin , Aleksandr Grafov , Veronika Nikitina , "Construction of Lorenz Curves Based on Empirical Distribution Laws of Economic Indicators," Mathematics and Statistics, Vol. 8, No. 6, pp. 637 - 644, 2020. DOI: 10.13189/ms.2020.080603.

(b). APA Format:
Aleksandr Bochkov , Dmitrii Pervukhin , Aleksandr Grafov , Veronika Nikitina (2020). Construction of Lorenz Curves Based on Empirical Distribution Laws of Economic Indicators. Mathematics and Statistics, 8(6), 637 - 644. DOI: 10.13189/ms.2020.080603.