SOME RESULTS ON ORDERING OF LORENZ AND RELATED CURVES FOR POWER FUNCTION DISTRIBUTION

The power function distribution is often used to study the electrical component reliability and also exhibits a better fit for failure data and provide more appropriate information about reliability and hazard rates. In the context of income inequality, some characterization of power function distribution is given in terms of its Lorenz curve. In this paper, necessary and sufficient conditions have been derived for dominance of Lorenz curve and related inequality curves in case of power function distribution. It is shown that the Lorenz curve for power function distribution is not symmetric but is skewed towards (1, 1). The moments of the Lorenz curve are also derived in case of power function distribution along with some welfare interpretations. Some interrelation among various ordering is also pointed out.