Evolutionary model of the personal income distribution

The aim of this work is to develop a qualitative picture of the personal income distribution. Treating an economy as a self-organized system the key idea of the model is that the income distribution contains competitive and non-competitive contributions. The presented model distinguishes between three main income classes. 1. Capital income from private firms is shown to be the result of an evolutionary competition between products. A direct consequence of this competition is Gibrat’s law suggesting a lognormal income distribution for small private firms. Taking into account an additional preferential attachment mechanism for large private firms the income distribution is supplemented by a power law (Pareto) tail. 2. Due to the division of labor a diversified labor market is seen as a non-competitive market. In this case wage income exhibits an exponential distribution. 3. Also included is income from a social insurance system. It can be approximated by a Gaussian peak. A consequence of this theory is that for short time intervals a fixed ratio of total labor (total capital) to net income exists (Cobb–Douglas relation). A comparison with empirical high resolution income data confirms this pattern of the total income distribution. The theory suggests that competition is the ultimate origin of the uneven income distribution.     

Power law tails in the Italian personal income distribution

We investigate the shape of the Italian personal income distribution using microdata from the Survey on Household Income and Wealth, made publicly available by the Bank of Italy for the years 1977–2002. We find that the upper tail of the distribution is consistent with a Pareto-power law type distribution, while the rest follows a two-parameter lognormal distribution. The results of our analysis show a shift of the distribution and a change of the indexes specifying it over time. As regards the first issue, we test the hypothesis that the evolution of both gross domestic product and personal income is governed by similar mechanisms, pointing to the existence of correlation between these quantities. The fluctuations of the shape of income distribution are instead quantified by establishing some links with the business cycle phases experienced by the Italian economy over the years covered by our dataset.     

Household income distribution in the USA

In this article we present an alternative model for the distribution of household incomesin the United States. We provide arguments from two differing perspectives which bothyield the proposed income distribution curve, and then fit this curve to empirical data onhousehold income distribution obtained from the United States Census Bureau.     

The Gompertz-Pareto income distribution

This work analyzes the Gompertz-Pareto distribution (GPD) of personal income, formed by the combination of the Gompertz curve, representing the overwhelming majority of the economically less favorable part of the population of a country, and the Pareto power law, which describes its tiny richest part. Equations for the Lorenz curve, Gini coefficient and the percentage share of the Gompertzian part relative to the total income are all written in this distribution. We show that only three parameters, determined by linear data fitting, are required for its complete characterization. Consistency checks are carried out using income data of Brazil from 1981 to 2007 and they lead to the conclusion that the GPD is consistent and provides a coherent and simple analytical tool to describe personal income distribution data.     

Zipf's law in income distribution of companies

Distribution functions of annual income of companies are analyzed based on two company databases. A clear power law distribution consistent with the Zipf's law can be confirmed for Japanese companies over more than three decades in income scale. Similar distributions can be confirmed in some other countries. It is confirmed that such power laws hold in most of job categories with slightly modified exponents. An annual income of a company is about two orders of magnitude smaller than its total assets, and the growth rate distribution of income is nearly independent of the income size in contrast to the case of growth rate of assets.     

Evidence for the exponential distribution of income in the USA

Using tax and census data, we demonstrate that the distribution of individual income in the USA is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8 = 0.375 calculated for two-earners families. Received 21 August 2000     

An statistical analysis of stratification and inequity in the income distribution

The analysis of the USA 2001 income distribution shows that it can be described by at least two main components, which obey the generalized Tsallis statistics with different values of the q parameter. Theoretical calculations using the gas kinetics model with a distributed saving propensity factor and two ensembles reproduce the empirical data and provide further information on the structure of the distribution, which shows a clear stratification. This stratification is amenable to different interpretations, which are analyzed. The distribution function is invariant with the average individual income, which implies that the inequity of the distribution cannot be modified by increasing the total income.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces, respectively. Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations. We study the influence of the inter-particle potentials. The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields. Moreover, the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles. These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

A study on the distribution of adsorbed nanoparticles

We use Monte Carlo simulation to calculate the distributions of particles under adsorption force near planar and cylindrical surfaces,respectively.Both hard sphere interaction and repulsive Yukawa (screened coulomb) interaction are employed in our simulations.We study the influence of the inter-particle potentials.The difference between the MC simulation results and the analytical results of ideal gas model shows that the interaction between particles plays an important role in the density distribution under external fields.Moreover,the 2-dimensional constructions of particles close to the surface are studied and show relations of the interaction between particles.These results may indicate us how to improve the methods of building nanoparticle coatings and nano-scale patterns.     

A study of the time distribution of inter-cluster earthquakes in Taiwan

In this study, we analyze the time distribution of inter-cluster earthquakes in Taiwan to infer correlation of earthquake occurrences. Our study based on the Diffusion Entropy Analysis (DEA) shows that there is positive correlation when the event time series is sampled by a time unit ranging from 120 to 1800 min. Also in the range of the time unit, two-slope feature in the determination of scaling exponent in DEA is observed, and the scenario is demonstrated by the simulations of synthetic earthquake sequence generated by the Copying Mistake Map model. Our simulation suggests that the earthquake sequence may consist of a randomness sequence and a correlated sequence, and the latter contributes to the correlation observed in our analysis.     

A study on the solubility and distribution of carbon in oxides

Measurements of radiocarbon in oxides were conducted after annealing single crystalline und polycrystalline FeO, Fe₃O₄, MnO, MgO, Cr₂O₃ and Al₂O₃ in radioactive CO₂-CO mixtures at 1000°C for different times. Concentrations of ≥ 0.01 wt. ppm C could be detected by anticoincidence counting and the distribution was observed by autoradiography. The measurements showed no carbon (< 0.01 ppm) in the lattice or the grain boundaries of pore- and crack-free oxides, carbon was detected only in cracks, pores or in grain boundaries which had cracked open. Thus, there is no measurable solubility of carbon in the bulk oxides for all the different chemical compositions investigated. Permeation of carbon through oxide layers on metals and alloys can only occur by transport of carbon-bearing molecules through cracks and pores of the oxide.     

A numerical study of the distribution of different attractors in the parameter space

A shooting technique for calculating the bifurcation curves of periodic solutions is described in this paper. This method is applied to the simple pendulum system leading to a parameter space divided into numerous regions of different attractors, and the results obtained are compared with available harmonic balance solutions. The coexistence of two or more periodic attractors is indicated, and a fractal attracting basin structure is revealed.     

A preliminary study of the distribution of plankton using hologrammetry

The distribution and dynamics of particles in the aquatic environment play an important role in the modelling of bio-geochemical processes. Previous work on the measurement of such particles, which vary in size from tens of micrometres (individual cells) to several centimetres (aggregates such as ‘marine snow’), has mainly used electronic counting or conventional photography coupled with image analysis. Here we report on an initial study of the use of holographic mensuration, otherwise known as hologrammetry, for the enumeration, sizing and spatial distribution determination of plankton. We present results on imaging plankton in water tanks using both in-line and off-axis pulsed-laser holography. In this work, we have recorded in-line holograms in a volume of 2400 cm³ of water with a resolution of better than 20 μm and off-axis holograms in a volume of 36000 cm³ with a resolution of 140 μm. In both cases, identifiable images of plankton were obtained and precise spatial coordinates determined from the in-line holograms.     

Experimental study of the noise emission of personal computer cooling fans

A controlled experimental study of the noise emission of a typical model of computer cooling fan, under different operating conditions, was done. The sound-power levels and directivities of 80-mm-diameter Panaflo computer fans mounted in a test plenum were determined from measurements of sound-pressure level over a hemi-spherical surface above a reflecting plane. The design and testing of the test plenum is discussed. Results of tests performed on one fan unit to gain an understanding of the fan’s noise-radiation characteristics and how they vary with operating conditions are presented. The results show that the noise emission of the Panaflo fan is directly related to the voltage and inversely related to the air-flow rate. It was found that the noise level measured at one particular position corresponds well to the average of those measured at 10 points on the hemisphere. The variability of the noise radiation from these Panaflo fans was determined by testing three other fans; variations of resulting total A-weighted power levels were within 1 dB.     

Cems study of the carbon distribution in austenite

CEMS resolution allows a careful study of Fe−C pure austenite spectra with high carbon content. Three Fe environments are detected which are ascribed to Fe atoms with one carbon first nearest neighbour and zero carbon second nearest neighbour and two environments with no carbon first nearest neighbour but zero carbon second nearest neighbour and one to four carbon second nearest neighbours respectively. This confirms the repulsive interaction between carbon interstitials and the tendency towards Fe₈C ordering is suggested.     

Vertical distribution of traffic noise—A preliminary study

This paper examines the effect of flight on the sound radiated by a high frequency source embedded in a constant area jet pipe in the presence of flow. Ray acoustics theory and classical results for sound transmission at an interface of relative motion are used. The diffraction of sound at the nozzle lips, the inhomogeneity and irregularity of the interface and the possibility of instability waves being triggered by the incident sound are neglected. Some of the waves characterized by wave-fronts pointing upstream are shown to be convected downstream by the flow and to illuminate the forward arc after refraction at the jet interface. The amount of energy emitted by the source, which is trapped inside the flow, depends only on internal jet pipe conditions. However, the portion of the forward arc which is illuminated by this energy, is a function of flight speed. The radiation into the ambient atmosphere at rest of a basically omnidirectional source peaks at the edge of the downstream zone of silence and falls off rapidly when the observation angle is increased. The flight to static comparison reveals an interesting forward arc amplification due to flight but this occurs in a range of angles where the radiation is basically rather feeble.