We study multiplicative and affine sequences of real numbers defined byN(j+1)=ζ(j)N(j)+η(j),where {ζ(j)} and {η(j)} are sequences of positive real numbers (in the multiplicative case η(j)=0 for all j). We investigate the conditions under which the leading digits k of {N(j)} have the...

We study the finite-size effects in some scaling systems, and show that the finite number of agents N leads to a cut-off in the upper value of the Pareto law for the relative individual wealth. The exponent α of the Pareto law obtained in stochastic multiplicative market models is crucially...

Using the uniform most powerful unbiased test, we observed the sales distribution of consumer electronics in Japan on a daily basis and report that it follows both a lognormal distribution and a power-law distribution and depends on the state of the market. We show that these switches occur...

Pareto's law states that the distribution of personal income obeys a power-law in the high income range. Its dynamical nature has been little studied hitherto, mostly due to the lack of empirical work. Using an exhaustive list of taxpayers in Japan for two consecutive years, when the economy was...

We find that area and population distributions of nations follow an inverse power-law, as is known for cities, but with a different exponent. To interpret this result, we develop a growth model based on the geometrical properties of partitioning of the plane. The substantial agreement between...

This paper discusses the size distribution–in economic terms–of the Italian municipalities over the period 2007–2011. Yearly data are rather well fitted by a modified Lavalette law, while Zipf–Mandelbrot–Pareto law seems to fail in this doing. The analysis is performed either at a...

Zipf’s law can be used to describe the rank-size distribution of cities in a region. It has seldom been employed to research urban internal structure. In this paper, we demonstrate that the space-filling process within a city follows Zipf’s law and can be characterized with the rank-size...

We present a statistical model for the distribution of Chinese names. Both family names and given names are studied on the same basis. With naive expectation, the distribution of family names can be very different from that of given names. One is affected mostly by genealogy, while the other can...

In this paper we report the existence of long-range memory in the opening moves of a chronologically ordered set of chess games using an extensive chess database. We used two mapping rules to build discrete time series and analyzed them using two methods for detecting long-range correlations;...

This paper formulates a random-growth urban model with a notion of geographical fitness. Using techniques of complex-network theory, we study our system as a type of preferential-attachment model with fitness, and we analyze its macro behavior to clarify the properties of the city-size...