This note revisits the ideas of the so-called semiparametric methods that we consider to be very useful when applying machine learning in insurance. To this aim, we first recall the main essence of semiparametrics like the mixing of global and local estimation and the combining of explicit...

Power laws appear widely in many branches of economics, geography, demography and other social sciences. In particular, the upper tail of city size distributions appear to follow power laws, as many researchers have shown for different countries and different periods of times. A crucial point in...

In a recent paper Rohde (2009) proposes a new functional form for estimating the Lorenz curve. This paper demonstrates that the model proposed by Rohde is a reparameterization of the model proposed by Aggarwal (1984). New and important properties of the model are established.

Let L0 consider an initial Lorenz curve. In this paper we propose a general methodology for obtaining new classes of parametric Lorenz or Leimkuhler curves that contain the original curve as limiting or special case. The new classes introduce additional parameters in the original family,...

The study of the informetric distributions, such as distributions of citations and impact factors is one of the most relevant topics in the current informetric research. Several laws for modeling impact factor based on ranks have been proposed, including Zipf, Lavalette and the two-exponent law...

The Pareto-positive stable (PPS) distribution is introduced as a new model for describing city size data in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data, where zero and unimodality are possible, and the classical Pareto and...