An application of Lorenz Curve in the study of population inequality

The Lorenz Curve is used in the description and comparison of the concentration of several income variables. In this paper we propose it's utilization to analyze the concentration of the population over some land surfaces. For the purpose of establishing priorities in political stratigies of environmental performance, it can be interesting to compare the degree of spatial concentration of the population that lives outside large cities. We can then compare, using the Lorenz curve, the correct truncated distributions of the populational size for different regions. We present sufficient conditions for the Lorenz order of two right truncated random variables, which does not involve the inverse distribution functions, and we will apply our results to the Pareto distributions.