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

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  • Gheorghiță Zbăganu

    (“Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics, 050711 Bucharest, Romania)

Abstract

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.

Suggested Citation

  • Gheorghiță Zbăganu, 2020. "Asymptotic Results in Broken Stick Models: The Approach via Lorenz Curves," Mathematics, MDPI, vol. 8(4), pages 1-29, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:625-:d:347229
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    References listed on IDEAS

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    1. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    2. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
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