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Open AccessArticle

Asymptotic Results in Broken Stick Models: The Approach via Lorenz Curves

“Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania
Mathematics 2020, 8(4), 625; https://doi.org/10.3390/math8040625
Received: 29 January 2020 / Revised: 1 April 2020 / Accepted: 7 April 2020 / Published: 18 April 2020
(This article belongs to the Special Issue Probability, Statistics and Their Applications)
A stick of length 1 is broken at random into n smaller sticks. How much inequality does this procedure produce? What happens if, instead of breaking a stick, we break a square? What happens asymptotically? Which is the most egalitarian distribution of the smaller sticks (or rectangles)? Usually, when studying inequality, one uses a Lorenz curve. The more egalitarian a distribution, the closer the Lorenz curve is to the first diagonal of [ 0 , 1 ] 2 . This is why in the first section we study the space of Lorenz curves. What is the limit of a convergent sequence of Lorenz curves? We try to answer these questions, firstly, in the deterministic case and based on the results obtained there in the stochastic one. View Full-Text
Keywords: broken stick; Lorenz curve; Gini coefficient; weak convergence broken stick; Lorenz curve; Gini coefficient; weak convergence
MDPI and ACS Style

Zbăganu, G. Asymptotic Results in Broken Stick Models: The Approach via Lorenz Curves. Mathematics 2020, 8, 625.

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