5 research outputs found
The uniqueness of company size distribution function from tent-shaped growth rate distribution
We report the proof that the extension of Gibrat's law in the middle scale
region is unique and the probability distribution function (pdf) is also
uniquely derived from the extended Gibrat's law and the law of detailed
balance. In the proof, two approximations are employed. The pdf of growth rate
is described as tent-shaped exponential functions and the value of the origin
of the growth rate distribution is constant. These approximations are confirmed
in profits data of Japanese companies 2003 and 2004. The resultant profits pdf
fits with the empirical data with high accuracy. This guarantees the validity
of the approximations.Comment: 6 pages, 5 figure
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
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
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