Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series B, Pt. 1, 130--134

A CHARACTERIZATION OF THE $\ALPHA$-MIXTURE PARETO DISTRIBUTION THROUGH A PROPERTY OF LORENZ CURVE

By

T. S. K. MOOTHATHU, University of Kerala

 

SUMMARY. We show that the $\alpha$-mixture Pareto distribution is the only distribution with the property that the Lorentz curve of the distribution truncated on the right at a point below the $\alpha$-th quantile and that of the distribution truncated on the left at a point above the $\alpha$-th quantile are independent of points of truncation.

AMS(1980)subject classification. 62E10, 60E10, 62P99

Key words and phrases. Cauchy functional equation, inverse Pareto distribution, Pareto distribution, truncated distribution.

FULL PAPER.

This article in Mathematical Reviews.