Functional Form for Estimating the Lornez Curve

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Functional Form for Estimating the Lornez Curve BIJAN BIDABAD WSEAS Post Doctorate Researcher No. 2, 12th St., Mahestan Ave., Shahrak Gharb, Tehran, 14658 IRAN bijan@bidabad.com http://www.bidabad.com BEHROUZ BIDABAD Faculty of mathematics, Polytechnics University, Hafez Ave., Tehran, 15914 bidabad@aut.ac.ir http://www.aut.ac.ir/official/main.asp?uid=bidabad NIKOS MASTORAKIS Technical University of Sofia, Department of Industrial Engineering, Sofia, 1000 BULGARIA mastor@tu-sofia.bg http://elfe.tu-sofia.bg/mastorakis

Abstract A flexible Lorenz curve which offers different curvatures allowed by the theory of income distribution is introduced. The intrinsically autoregressive nature of the errors in cumulative data of the Lorenz curve is also under consideration.

Introduction Income distribution is often portrayed on a Lorenz curve. In recent years some of its functional forms have been introduced. These forms should satisfy some definitional properties, and also make estimation of the function parameters by the known estimating methods simple. This note emphasizes on two other characteristics of the Lorenz curve which have been neglected.

First, Lorenz curve could be non-symmetric with respect to the line y=1-x, for 0≤x≤1. This enables that different Lorenz curves cross the others which are the same in functional form and different in parameters for 0<x<1). M. R. Gupta (1) proposed the following definitional properties. The function y=f(x) represents the Lorenz curve, if:

Proposition

Second thing that has been ignored is the autoregressive nature of the errors in the Lorenz curve data. On the other hand, when there is an error in the (𝑡−1)th percent of income earners, this error completely will transfer to the next cumulative percent (t). This is because of using cumulative data to estimate the Lorenz curve.

Functional Form for Estimating the Lornez Curve BIJAN BIDABAD WSEAS Post Doctorate Researcher No. 2, 12th St., Mahestan Ave., Shahrak Gharb, Tehran, 14658 IRAN bijan@bidabad.com http://www.bidabad.com BEHROUZ BIDABAD Faculty of mathematics, Polytechnics University, Hafez Ave., Tehran, 15914 bidabad@aut.ac.ir http://www.aut.ac.ir/official/main.asp?uid=bidabad NIKOS MASTORAKIS Technical University of Sofia, Department of Industrial Engineering, Sofia, 1000 BULGARIA mastor@tu-sofia.bg http://elfe.tu-sofia.bg/mastorakis