共查询到20条相似文献,搜索用时 15 毫秒
1.
G.-F. Gu W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,67(4):585-592
Recently, Mike and Farmer have constructed a very powerful
and realistic behavioral model to mimick the dynamic process of
stock price formation based on the empirical regularities of order
placement and cancelation in a purely order-driven market, which can
successfully reproduce the whole distribution of returns, not only
the well-known power-law tails, together with several other
important stylized facts. There are three key ingredients in the
Mike-Farmer (MF) model: the long memory of order signs characterized
by the Hurst index Hs, the distribution of relative order prices
x in reference to the same best price described by a Student
distribution (or Tsallis’ q-Gaussian), and the dynamics of order
cancelation. They showed that different values of the Hurst index
Hs and the freedom degree αx of the Student distribution
can always produce power-law tails in the return distribution
fr(r) with different tail exponent αr. In this paper, we
study the origin of the power-law tails of the return distribution
fr(r) in the MF model, based on extensive simulations with
different combinations of the left part L(x) for x < 0 and the
right part R(x) for x > 0 of fx(x). We find that power-law
tails appear only when L(x) has a power-law tail, no matter R(x)
has a power-law tail or not. In addition, we find that the
distributions of returns in the MF model at different timescales can
be well modeled by the Student distributions, whose tail exponents
are close to the well-known cubic law and increase with the
timescale. 相似文献
2.
We study message transfer in a 2-d communication network of regular nodes and randomly distributed hubs. We study both single
message transfer and multiple message transfer on the lattice. The average travel time for single messages travelling between
source and target pairs of fixed separations shows q-exponential behaviour as a function of hub density with a characteristic power-law tail, indicating a rapid drop in the average
travel time as a function of hub density. This power-law tail arises as a consequence of the log-normal distribution of travel
times seen at high hub densities. When many messages travel on the lattice, a congestion-decongestion transition can be seen.
The waiting times of messages in the congested phase show a Gaussian distribution, whereas the decongested phase shows a log-normal
distribution. Thus the waiting time distributions carry the signature of congested or decongested behaviour.
相似文献
3.
D.G. Xenikos 《Physica A》2009,388(23):4910-4918
In this report we study the dynamics characteristics of conversations among several participants, analyzing trunked mobile telephony databases. We find that the duration of the dialogue sessions deviates systematically from the predictions of Poisson statistics, following probability distributions with either log-normal or power law tail. We propose that such a behavior can be described using the Bouchaud-Mezard (B-M) stochastic model, which suggests that the two probability distributions correspond to different types of human networking in conversations. We discuss the implications of our results in risk assessment in communications. 相似文献
4.
Qing Wang 《Physica A》2010,389(10):2127-2133
In recent years, the study of power-law scaling characteristics of real-life networks has attracted much interest from scholars; it deviates from the Poisson process. In this paper, we take the whole process of aerial inbound operation in a logistics company as the empirical object. The main aim of this work is to study the statistical scaling characteristics of the task-restricted work patterns. We found that the statistical variables have the scaling characteristics of unimodal distribution with a power-law tail in five statistical distributions — that is to say, there obviously exists a peak in each distribution, the shape of the left part closes to a Poisson distribution, and the right part has a heavy-tailed scaling statistics. Furthermore, to our surprise, there is only one distribution where the right parts can be approximated by the power-law form with exponent α=1.50. Others are bigger than 1.50 (three of four are about 2.50, one of four is about 3.00). We then obtain two inferences based on these empirical results: first, the human behaviors probably both close to the Poisson statistics and power-law distributions on certain levels, and the human-computer interaction behaviors may be the most common in the logistics operational areas, even in the whole task-restricted work pattern areas. Second, the hypothesis in Vázquez et al. (2006) [A. Vázquez, J. G. Oliveira, Z. Dezsö, K.-I. Goh, I. Kondor, A.-L. Barabási. Modeling burst and heavy tails in human dynamics, Phys. Rev. E 73 (2006) 036127] is probably not sufficient; it claimed that human dynamics can be classified as two discrete university classes. There may be a new human dynamics mechanism that is different from the classical Barabási models. 相似文献
5.
利用中国气象局国家气候中心740站点1960—2000年日降水观测资料,统计分析表明,各气候特征区30 mm以上日降水存在幂律尾分布特征,从中国的整体情况来看,幂律尾指数的均值超过了3.0,其对应的降水过程不存在平稳性成分,因此长期暴雨预报成为一个艰巨的任务.借助滤波方法进一步研究发现:日降水幂律尾分布特征是大气中各尺度系统相互作用的结果,其中一周尺度系统对30 mm以上日降水幂律尾指数影响最大.
关键词:
幂律尾指数
传递熵
暴雨 相似文献
6.
G. Cevolani G. Trivellone G. Bortolotti C. Franceschi S. Gottardi G. Grassi S. P. Kingsley 《Il Nuovo Cimento C》1993,16(3):255-263
Summary The distribution of the energy reflected by a meteor trail is strongly connected to the ionization density distribution across
and along a meteor trail. Recent forward-scatter observations over the Bologna-Lecce baseline in Italy carried out in 1991–92,
show that the number of underdense meteor trails (with electron line densityq≤2.1014 electrons/mvs. peak signal amplitudes decreases more rapidly with the increasing signal level than what predicted. An exponential (simple
and/or log-normal) model is proposed, by taking into account different signal-to-noise ratio thresholds and the Kolmogorov-Smirnov
(K-S) procedure is used to test the overall goodness of fit between the set of observations and specified theoretical distributions.
It is shown that this model provides a better fit to data mainly for middle-high levels of received power and for values ofq≥1013 electrons/m. 相似文献
7.
G.-H. Mu W. Chen J. Kertész W.-X. Zhou 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,68(1):145-152
The distributions of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese
stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individualstocks
exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the
“q-Gamma” function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of tradingvolumes at
different timescales Δt ranging from 1 min to 240 min can be well modeled. The applicability of the q-Gamma functions for
multiple trades is restricted to the transaction numbers Δn≤ 8. We find that all the PDFs have power-law tails for large volumes.
Using careful estimation of the average tail exponents α of the distributions of trade sizes and trading volumes, we get α>
2, well outside the Lévy regime. 相似文献
8.
9.
A network induced by wealth is a social network model in which wealth induces individuals to participate as nodes, and every node in the network produces and accumulates wealth utilizing its links. More specifically, at every time step a new node is added to the network, and a link is created between one of the existing nodes and the new node. Innate wealth-producing ability is randomly assigned to every new node, and the node to be connected to the new node is chosen randomly, with odds proportional to the accumulated wealth of each existing node. Analyzing this network using the mean value and continuous flow approaches, we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node. From this relation, we show that the degree distribution of the network induced by wealth is scale-free. We also show that the wealth distribution has a power-law tail and satisfies the 80/20 rule. We also show that, over the whole range, the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the Bouchaud-Mèzard model, even though the mechanism for producing wealth is quite different in our model. Further, we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log-normal distribution, while for the richest, the cumulative wealth distribution has a power-law behavior. 相似文献
10.
The goal of developing a firmer theoretical understanding of inhomogeneous temporal processes–in particular, the waiting times in some collective dynamical system–is attracting significant interest among physicists. Quantifying the deviations between the waiting-time distribution and the distribution generated by a random process may help unravel the feedback mechanisms that drive the underlying dynamics. We analyze the waiting-time distributions of high-frequency foreign exchange data for the best executable bid–ask prices across all major currencies. We find that the lognormal distribution yields a good overall fit for the waiting-time distribution between currency rate changes if both short and long waiting times are included. If we restrict our study to long waiting times, each currency pair’s distribution is consistent with a power-law tail with exponent near to 3.5. However, for short waiting times, the overall distribution resembles one generated by an archetypal complex systems model in which boundedly rational agents compete for limited resources. Our findings suggest that a gradual transition arises in trading behavior between a fast regime in which traders act in a boundedly rational way and a slower one in which traders’ decisions are driven by generic feedback mechanisms across multiple timescales and hence produce similar power-law tails irrespective of currency type. 相似文献
11.
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of distributions are used, namely a distribution derived from the Mittag-Leffler survival function and the Weibull distribution. For the Mittag-Leffler type distribution, the average waiting time (residual life time) is strongly dependent on the choice of a cut-off parameter tmax, whereas the results based on the Weibull distribution do not depend on such a cut-off. Therefore, a Weibull distribution is more convenient than a Mittag-Leffler type if one wishes to evaluate relevant statistics such as average waiting time in financial markets with long durations. On the other hand, we find that the Gini index is rather independent of the cut-off parameter. Based on the above considerations, we propose a good candidate for describing the distribution of first-passage time in a market: The Weibull distribution with a power-law tail. This distribution compensates the gap between theoretical and empirical results more efficiently than a simple Weibull distribution. It should be stressed that a Weibull distribution with a power-law tail is more flexible than the Mittag-Leffler distribution, which itself can be approximated by a Weibull distribution and a power-law. Indeed, the key point is that in the former case there is freedom of choice for the exponent of the power-law attached to the Weibull distribution, which can exceed 1 in order to reproduce decays faster than possible with a Mittag-Leffler distribution. We also give a useful formula to determine an optimal crossover point minimizing the difference between the empirical average waiting time and the one predicted from renewal theory. Moreover, we discuss the limitation of our distributions by applying our distribution to the analysis of the BTP future and calculating the average waiting time. We find that our distribution is applicable as long as durations follow a Weibull law for short times and do not have too heavy a tail. 相似文献
12.
J.-J. Tseng S.-P. Li S.-C. Wang 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,73(1):69-74
We conduct a market experiment with human agents in order to explore the structure of transaction networks and to study the dynamics of wealth accumulation. The experiment is carried out on our platform for 97 days with 2,095 effective participants and 16,936 times of transactions. From these data, the hybrid distribution (log-normal bulk and power-law tail) in the wealth is observed and we demonstrate that the transaction networks in our market are always scale-free and disassortative even for those with the size of the order of few hundred. We further discover that the individual wealth is correlated with its degree by a power-law function which allows us to relate the exponent of the transaction network degree distribution to the Pareto index in wealth distribution. 相似文献
13.
Alessandro Garavaglia Remco van der Hofstad Gerhard Woeginger 《Journal of statistical physics》2017,168(6):1137-1179
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive. 相似文献
14.
The mass spectra of both light and heavy mesons are studied in the Dirac equation with an equally mixed 4-vector and scalar
power-law potential model. This potential provides an excellent fit not only to the mass spectra ofp°, ϕ, Ψ and υ families but also to those ofD, F andB mesons. The light quark masses inp° and ϕ as well as in atom-like mesons are very close to the current quark masses. 相似文献
15.
J. Lorenz 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,71(2):251-258
In this paper histograms of user ratings for movies
(1
\bigstar\bigstar,...,10
\bigstar\bigstar) are analysed. The evolving stabilised shapes of
histograms follow the rule that all are either double- or triple-peaked.
Moreover, at most one peak can
be on the central bins 2
\bigstar\bigstar,...,9
\bigstar\bigstar and the distribution in these
bins looks smooth `Gaussian-like’ while changes at the extremes (1
\bigstar\bigstar and
10
\bigstar\bigstar) often look
abrupt. It is shown that this is well approximated under the assumption that
histograms are
confined and discretised probability density functions of Lévy skew
α-stable distributions. These distributions are the only stable
distributions which could emerge due to a generalized central limit theorem from
averaging of various independent random variables as which one can see the
initial
opinions of users. Averaging is also an appropriate assumption about the social
process which underlies the process of continuous opinion formation.
Surprisingly, not the normal distribution achieves the best fit over histograms
observed on the web, but distributions with fat tails which decay as power-laws
with exponent –(1+α)
(a = \frac43)(\alpha=\frac{4}{3}). The scale and skewness
parameters of the Lévy
skew α-stable distributions seem to depend on the deviation from an
average movie (with mean about 7.6
\bigstar\bigstar). The histogram of such an average
movie
has no skewness and is the most narrow one. If a movie deviates from average the
distribution gets broader and skew. The skewness pronounces the deviation.
This is used to construct a one parameter fit which gives some evidence of
universality in processes of continuous opinion dynamics about taste. 相似文献
16.
F. Pammolli D. Fu S. V. Buldyrev M. Riccaboni K. Matia K. Yamasaki H. E. Stanley 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(2):127-130
We introduce a model of proportional growth to explain the distribution P(g) of business firm growth rates. The model predicts
that P(g) is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ζ = 3.
Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body
of the distribution. We test the model at different levels of aggregation in the economy, from products, to firms, to countries,
and we find that the predictions are in good agreement with empirical evidence on both growth distributions and size-variance
relationships. 相似文献
17.
For the study of citation networks, a challenging problem is modeling the high clustering. Existing studies indicate that the promising way to model the high clustering is a copying strategy, i.e., a paper copies the references of its neighbor as its own references. However, the line of models highly underestimates the number of abundant triangles observed in real citation networks and thus cannot well model the high clustering. In this paper, we point out that the failure of existing models lies in that they do not capture the connecting patterns among existing papers. By leveraging the knowledge indicated by such connecting patterns, we further propose a new model for the high clustering in citation networks. Experiments on two real world citation networks, respectively from a special research area and a multidisciplinary research area, demonstrate that our model can reproduce not only the power-law degree distribution as traditional models but also the number of triangles, the high clustering coefficient and the size distribution of co-citation clusters as observed in these real networks. 相似文献
18.
Blinking of single molecules and nanocrystals is modeled as a two-state renewal process with on (fluorescent) and off (non-fluorescent)
states. The on and off-times may have power-law or exponential distributions. A fractional generalization of the exponential
function is used to develop a unified treatment of the blinking statistics for both types of distributions. In the framework
of the two-state model, an equation for the probability density p(t
on|t) of the total on-time is derived. As applied to power-law blinking, the equation contains derivatives of fractional orders
α and β equal to the exponents of the on and off-time power-law distributions, respectively. In the limit case of α = β =
1, the distributions become exponential and the fractional differential equation reduces to an integer order differential
equation. Solutions to these equations are expressed in terms of fractional stable distributions. The Poisson transform of
p(t
on|t) is the photon number distribution that determines the photon counting statistics. It is shown that the long-time asymptotic
behavior of Mandel’s Q parameter follows a power law: M(t) ∝ t
γ
. The function γ(α, β) is defined on the (α, β) plane. An analysis of the relative variance of the total on-time shows that it decays only
when α = β = 1 or α < β. Otherwise, relative fluctuations either exhibit asymptotic power-law growth or approach a constant
level. Analytical calculations are in good agreement with the results of Monte Carlo simulations. 相似文献
19.
With income data from Chinese household income projects in 1998-2002, we study the functional form of Chinese income distribution. The fitting results suggest a log-normal distribution plus a power-law tail. This distributional form has changed a lot from its appearance in the early stage of China's reform and turns out to be consistent with that of some complete market economies. The uncertainty and diversity of income growth rate aroused by marketing reform are the main causes of current Chinese income distribution. 相似文献
20.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2009,70(3):413-433
We discuss the distribution of the gravitational force
created by a Poissonian distribution of field sources (stars,
galaxies,...) in different dimensions of space d. In d = 3, when
the particle number N →+∞, it is given by a Lévy
law called the Holtsmark distribution. It presents an algebraic
tail for large fluctuations due to the contribution of the nearest
neighbor. In d = 2, for large but finite values of N, it is given
by a marginal Gaussian distribution intermediate between Gaussian
and Lévy laws. It presents a Gaussian core and an algebraic
tail. In d = 1, it is exactly given by the Bernouilli distribution
(for any particle number N) which becomes Gaussian for N ≫
1. Therefore, the dimension d = 2 is critical regarding the
statistics of the gravitational force. We generalize these results
for inhomogeneous systems with arbitrary power-law density profile
and arbitrary power-law force in a d-dimensional universe. 相似文献