At first glance lottery is a form of gambling, a game in which the chances of winning are extremely small. But upon a deeper look, considering that the Jackpot prize of lotteries is a result of the ...active participation of millions of players, we come to the conclusion that the interaction of the simple rules with the high number of players creates an emergent complex system. Such a system is characterized by its time-series that presents some interesting properties. Given the inherent stochastic nature of this game, it can be described within a mean-field type approach, such as the one implemented in the Local Growth and Global Reset (LGGR) model. We argue that the Jackpot time-series behaves ergodic for six lotteries with diverse formats and player pools. Specifying this consideration in the framework of the LGGR model, we model the lotteries with growth rates confirmed by the time-series. The reset rate is deduced mathematically and confirmed by data. Given these parameters, we calculate the probability density of the Jackpot prizes, that fits well the empirically observed ones. We propose to use a single w parameter, as the product of the player pools found under the jurisdiction of the lottery and the chance that a single lottery ticket wins.
A mean-field like stochastic evolution equation with growth and reset terms (LGGR model) is used to model wealth distribution in modern societies. The stationary solution of the model leads to an ...analytical form for the density function that is successful in describing the observed data for all wealth categories. In the limit of high wealth values the proposed density function has the accepted Tsallis–Pareto shape. Our results are in agreement with the predictions of an earlier approach based on a mean-field like wealth exchange process.
•A growth and reset master equation provides a simple description for the observed wealth distributions.•A compact density function is given to describe the wealth inequalities in modern societies.•A collapse of wealth distributions is observed when wealth is normalized to the average wealth.•Experimental data is analyzed for wealth inequalities in USA, Russia and France.•Similarities between wealth and income distributions are discussed.
We provide an analytically treatable model that describes in a unified manner income distribution for all income categories. The approach is based on a master equation with growth and reset terms. ...The model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level spanning a nine year period in the Cluj county (Romania). In agreement with our theoretical predictions we find that income distributions computed for several years collapse on a master-curve when a properly normalised income is considered. The Beta Prime distribution is appropriate to fit the collapsed data and it is shown that distributions derived for other countries are following similar trends with different fit parameters. The non-universal feature of the fit parameters suggests that for a more realistic modelling the model parameters have to be linked with specific socio-economic regulations.
•Income at all levels is modelled in a unified manner.•A master equation with growth and reset terms is used to model income inequalities.•Individual level and exhaustive income data are analysed in the perspective of the model.•The Beta-prime distribution describes well the whole income distribution curve.•After an appropriate scaling income distribution for different years collapse.
This study presents an econophysics based approach to the study of lotteries. By treating lotteries as complex systems we analyse the guiding dynamics of real-world lotteries. We found that the ...growth of the jackpot, that can be won, between two successive draws is proportional to its preceding value. This growth is best described as a linear function with two parameters a and b reflecting foundational player pool sales and the excitement generated by the current jackpot respectively. A computer simulation considering additional parameters (such as the price of a ticket: s, and the format of the lottery: p) is used to study the statistical features of simulated lotteries covering a vast parameter space. This approach enables us to construct a detailed map of how various parameters influence lottery behaviour by examining the statistical characteristics of the simulated lotteries. The findings emphasize the need for thoughtful pricing strategies in real-world lotteries and suggest that simulations can assist organizers in making informed decisions.
The Internet on the router level, is a complex network embedded in a geographical space. We provide experimental evidences suggesting that the average travel time for a message, with fixed length, ...increases roughly as the square root of the geographical distance. To understand this scaling law and other measurable topological properties of the Internet as a graph, we introduce and study a simple network model. The model is based on a few realistic socio-economic facts/assumptions and qualitatively reproduces the experimentally observed stylized facts.
Socio-economic inequalities derived from an exhaustive wealth distribution is studied in a closed geographical region from Transylvania (Romania). Exhaustive wealth data is computed from the ...agricultural records of the Sancraiu commune for three different economic periods. The data is spanning two different periods from the communist economy and gives a glance to the present situation after 31 years of free market economy in Romania. The local growth and reset model based on an analytically solvable master equation is used to describe the observed data. The model with realistically chosen growth and reset rates is successful in describing both the experimentally observed distributions and the inequality indexes (Lorenz curve, Gini coefficient, and Pareto point) derived from this data. The observed changes in the inequality measures are discussed in the context of the relevant socio-economic conditions.
Lightning flashes result in an instantaneous emission of electromagnetic (EM)
waves that encompass a broad spectrum of frequencies in the domain of radio
waves. The signature of these impulses in the ...region of the very low frequency
(VLF) of radio waves and bellow are called spherics. These impulsive signals
traverse great distances in the waveguide between the Earth's ionosphere and
its surface. Due to the abundance of lightnings the lower end of the EM
spectrum is dominated by the waveforms of these emission. It is called
atmospheric radio noise because of its origin. This article outlines a
straightforward approach for capturing spherics activity within the VLF radio
wave range. Employing data processing techniques, we pinpoint the timestamps of
spherics within time series data. The distribution of inter-spheric times is
analyzed across various detection threshold levels. Utilizing recordings
spanning two distinct years and seasons, we replicate the established form of
the inter-spheric time distribution described in the literature. Notably, we
demonstrate that by rescaling the time intervals between spherics with the mean
time for a specific recording and given detection threshold, the distributions
collapse to a master curve. This universal pattern is accurately characterized
by a single-parameter mean-scaled Gamma distribution. Additionally, we note the
similarities in the distribution of inter-spheric times with patterns found in
earthquake recurrence times.
Universalities and intriguing analogies in the statistics of avalanches are revealed for three physical systems defined on largely different length and energy scales. Earthquakes induced by tectonic ...scale dynamics, micro-scale level quakes observed from slipping crystallographic planes in metals and a one-dimensional, room-scale spring-block type Burridge-Knopoff model is studied from similar statistical viewpoints. The validity of the Gutenberg-Richter law for the probability density of the energies dissipated in the avalanches is proven for all three systems. By analysing data for three different seismic zones and performing acoustic detection for different Zn samples under deformation, universality for the involved scaling exponent is revealed. With proper parameter choices the 1D Burridge-Knopoff model is able to reproduce the same scaling law. The recurrence times of earthquakes and micro-quakes with magnitudes above a given threshold present again similar distributions and striking quantitative similarities. However, the 1D Burridge-Knopoff model cannot account for the correlations observed in such statistics.
Univerzalnosti i intrigantne analogije u statistici lavina otkrivene su za tri fizičkasustava definirana na uvelike različitim duljinama i energijskim skalama. Potresi uzroko-va ni dinamikom na tektonskoj skali, mikro-potresi koji nastaju na klizećim kristalografskimravnina u metalima i jednodimenzionalni Burridge-Knopoffov model opruga i blokova na skali sobe proučeni su sa sličnih statističkih stajališta. Valjanost Gutenberg-Richteroverelacije za gustoću vjerojatnosti energija disipirane u lavinama dokazana je za sva tri sustava. Analizom podataka za tri različita seizmički aktivna područja i detekcijom akustičkih valova za različite uzorke Zn pod deformacijom, otkrivena je univerzalnost za uključeni eksponent skaliranja. S pravilnim izborom parametara 1D Burridge-Knopoffovmodel može reproducirati isti zakon skaliranja. Vremena ponavljanja potresa i mikro-potresa s magnitudama iznad zadanog praga opet predstavljaju slične distribucije i zapanjujuće kvantitativne sličnosti. Međutim, 1D Burridge-Knopoffov model ne može objasniti korelacije opažene u takvim statistikama.
At a first glance lottery is a form of gambling, a game in which the chances of winning is extremely small. But upon a deeper look, considering that the Jackpot prize of lotteries is a result of the ...active participation of millions of players, we come to the conclusion that the interaction of the simple rules with the high number of players creates an emergent complex system. Such a system is characterized by its time-series that presents some interesting properties. Given the inherent stochastic nature of this game, it can be described within a mean-field type approach, such as the one implemented in the Local Growth and Global Reset (LGGR) model. We argue that the Jackpot time-series behaves ergodic for six lotteries with diverse formats and player pools. Specifying this consideration in the framework of the LGGR model, we model the lotteries with growth rates confirmed by the time-series. The reset rate is deduced mathematically and confirmed by data. Given these parameters we calculate the probability density of the Jackpot prizes, that fits well the empirically observed ones. We propose to use a single w parameter, as the product of the player pools found under the jurisdiction of the lottery and the chance that a single lottery ticket wins.
Socio-economic inequalities derived from an exhaustive wealth distribution is studied in a closed geographical region from Transylvania (Romania). Exhaustive wealth data is computed from the ...agricultural records of the Sancraiu commune for three different economic situations. The gathered data is spanning two different periods from the communist economy and the present situation after 31 years of free market economy in Romania. The local growth and reset model based on an analytically solvable master equation is used to describe the observed data. The model with realistically chosen growth and reset rates is successful in describing both the experimentally observed distributions and the inequality indexes (Lorenz curve, Gini coefficient and Pareto point) derived from this data. The observed changes in these inequality measures are discussed in the context of the relevant socio-economic conditions.
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