In order to study phenomenon in detail that income distribution follows Pareto law, we analyze database of high income companies in Japan. We find a quantitative relation between average capital of the companies and the Pareto index, that the average capital becomes larger the Pareto index becomes smaller. From this relation, we point out a possibility we can explain that Pareto index of compan...

This note analyzes some properties of the Pareto Type III distribution. A three parameter version original two distribution proposed by is introduced and both its density characteristic function are derived. The analytic expression inverse also obtained, together with an explicit moments any order. Finally, a simple statistical exercise proposed, designed to show reliability in describing asymp...

In the literature of analyzing extremes, both generalized Pareto distribution and Pareto distribution are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ the generalized Pareto distribution in case of knowing the sign of the extreme value index. In this pape...

Empirical studies have shown that the size distribution of firms can be described as a lognormal or Pareto distribution. However, these studies have focused on developed countries and little attention has been devoted to developing countries. Using the variable of number of employees as a measure of firm size, this paper investigates the shape of firm size distribution in the food & beverages i...

The Generalized Pareto Distribution is a very useful tool for modeling in many areas of economics, finance and insurance. The Generalized Pareto Distribution is commonly used for extreme value problems. Especially, the values which exceed the finite threshold, is the focus in extreme value problems like in insurance sector. The Generalized Pareto Distribution is well approach for modeling the s...

W propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding a maximally uniform representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise from modeling...