In this paper, we propose a bivariate extension of univariate composite (two-spliced) distributions defined by Pareto distribution for values larger than some thresholds and Gumbel on the complementary domain. The purpose is to capture behavior data consisting mainly small medium but also extreme values. Some properties proposed are presented. Further, two estimation procedures discussed illust...

Mobile phone data have been extensively used in the recent years to study social behavior. However, most of these studies are based on only partial data whose coverage is limited both in space and time. In this paper, we point to an observation that the bias due to the limited coverage in time may have an important influence on the results of the analyses performed. In particular, we observe si...

The Pareto distribution, or power-law distribution, has long been used to model phenomena in many fields, including wildfire sizes, earthquake seismic moments and stock price changes. Recent observations have brought the fit of the Pareto into question, however, particularly in the upper tail where it often overestimates the frequency of the largest events. This paper proposes a graphical self-...

Recent work drawing on data for large and small firms has shown a Pareto distribution of firm size. We mix a Gibrat-type growth process among incumbents with an exponential distribution of firm’s age, to obtain the empirical Pareto distribution. JEL codes: L20, L25

We show for CES demands with heterogeneous production costs that profit, revenue, and output distributions lie in the same class as the productivity distribution (e.g., the "Pareto circle"), although the price distribution lies in the inverse class. We relate distribution shapes via the elasticities of their densities. Introducing product quality decouples the CES circle. Then, all distribution...