8 research outputs found
Pareto law and Pareto index in the income distribution of Japanese companies
In order to study the phenomenon in detail that income distribution follows
Pareto law, we analyze the database of high income companies in Japan. We find
a quantitative relation between the average capital of the companies and the
Pareto index. The larger the average capital becomes, the smaller the Pareto
index becomes. From this relation, we can possibly explain that the Pareto
index of company income distribution hardly changes, while the Pareto index of
personal income distribution changes sharply, from a viewpoint of capital (or
means). We also find a quantitative relation between the lower bound of capital
and the typical scale at which Pareto law breaks. The larger the lower bound of
capital becomes, the larger the typical scale becomes. From this result, the
reason there is a (no) typical scale at which Pareto law breaks in the income
distribution can be understood through (no) constraint, such as the lower bound
of capital or means of companies, in the financial system.Comment: 12 pages, 8 figure
Pareto index induced from the scale of companies
Employing profits data of Japanese companies in 2002 and 2003, we confirm
that Pareto's law and the Pareto index are derived from the law of detailed
balance and Gibrat's law. The last two laws are observed beyond the region
where Pareto's law holds. By classifying companies into job categories, we find
that companies in a small scale job category have more possibilities of growing
than those in a large scale job category. This kinematically explains that the
Pareto index for the companies in the small scale job class is larger than that
for the companies in the large scale job class.Comment: 14 pages, 11 figure
Relations between a typical scale and averages in the breaking of fractal distribution
We study distributions which have both fractal and non-fractal scale regions
by introducing a typical scale into a scale invariant system. As one of models
in which distributions follow power law in the large scale region and deviate
further from the power law in the smaller scale region, we employ 2-dim quantum
gravity modified by the term. As examples of distributions in the real
world which have similar property to this model, we consider those of personal
income in Japan over latest twenty fiscal years. We find relations between the
typical scale and several kinds of averages in this model, and observe that
these relations are also valid in recent personal income distributions in Japan
with sufficient accuracy. We show the existence of the fiscal years so called
bubble term in which the gap has arisen in power law, by observing that the
data are away from one of these relations. We confirm, therefore, that the
distribution of this model has close similarity to those of personal income. In
addition, we can estimate the value of Pareto index and whether a big gap
exists in power law by using only these relations. As a result, we point out
that the typical scale is an useful concept different from average value and
that the distribution function derived in this model is an effective tool to
investigate these kinds of distributions.Comment: 17 pages, latex, 13 eps figure
Equivalent continuous and discrete realizations of Levy flights: Model of one-dimensional motion of inertial particle
The paper is devoted to the relationship between the continuous Markovian
description of Levy flights developed previously and their equivalent
representation in terms of discrete steps of a wandering particle, a certain
generalization of continuous time random walks. Our consideration is confined
to the one-dimensional model for continuous random motion of a particle with
inertia. Its dynamics governed by stochastic self-acceleration is described as
motion on the phase plane {x,v} comprising the position x and velocity v=dx/dt
of the given particle. A notion of random walks inside a certain neighbourhood
L of the line v=0 (the x-axis) and outside it is developed. It enables us to
represent a continuous trajectory of particle motion on the plane {x,v} as a
collection of the corresponding discrete steps. Each of these steps matches one
complete fragment of the velocity fluctuations originating and terminating at
the "boundary" of L. As demonstrated, the characteristic length of particle
spatial displacement is mainly determined by velocity fluctuations with large
amplitude, which endows the derived random walks along the x-axis with the
characteristic properties of Levy flights. Using the developed classification
of random trajectories a certain parameter-free core stochastic process is
constructed. Its peculiarity is that all the characteristics of Levy flights
similar to the exponent of the Levy scaling law are no more than the parameters
of the corresponding transformation from the particle velocity v to the related
variable of the core process. In this way the previously found validity of the
continuous Markovian model for all the regimes of Levy flights is explained
Derivation of the distribution from extended Gibrat's law
Employing profits data of Japanese companies in 2002 and 2003, we identify
the non-Gibrat's law which holds in the middle profits region. From the law of
detailed balance in all regions, Gibrat's law in the high region and the
non-Gibrat's law in the middle region, we kinematically derive the profits
distribution function in the high and middle range uniformly. The distribution
function accurately fits with empirical data without any fitting parameter.Comment: 13 pages, 8 figure