An empirical comparison of sales time series for online and offline channels for commodities in China

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
JINLONG WANG ◽  
CAN WEN ◽  
XIAOYI WANG
Keyword(s):  
Time Series ◽  
Complex Networks ◽  
Power Law ◽  
Constant Parameter ◽  
Power Law Distribution ◽  
Empirical Comparison ◽  
Visibility Graphs ◽  
Offline Channels ◽  
Power Law Distributions

In this paper we make an empirical comparison of sales time series for online and offline channels. In particular, we analyse the sales dynamic and fluctuation level underlying the sales time series in different channels. The accumulative daily sales distributions of commodities are analysed statistically and the daily sales series are also studied from the perspective of complex networks. We find that most of the commodities' accumulative sales distributions can be fitted by power-law distributions. Visibility graphs are constructed for the daily sales series, and the accumulative degree distributions are also investigated – it is found that they also almost follow power-law distribution. The constant parameter α indicates that different specifications of the same goods have different sales characteristics, and different forms of packaging of commodities, either special offer or ordinary, also show distinctive sales fluctuation levels. The differences show that the direction of these relationships is opposite for online and offline channels.

scholarly journals Predicting observational signatures of coronal heating by Alfvén waves and nanoflares

2007 ◽  
Vol 3 (S247) ◽  
pp. 279-287
Author(s):  
Patrick Antolin ◽  
Kazunari Shibata ◽  
Takahiro Kudoh ◽  
Daiko Shiota ◽  
David Brooks
Keyword(s):  
Power Law ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Power Law Distribution ◽  
Longitudinal Modes ◽  
Heating Mechanism ◽  
Set Up ◽  
Power Law Index ◽  
Power Law Distributions ◽  
Release Processes

AbstractAlfvén waves can dissipate their energy by means of nonlinear mechanisms, and constitute good candidates to heat and maintain the solar corona to the observed few million degrees. Another appealing candidate is the nanoflare-reconnection heating, in which energy is released through many small magnetic reconnection events. Distinguishing the observational features of each mechanism is an extremely difficult task. On the other hand, observations have shown that energy release processes in the corona follow a power law distribution in frequency whose index may tell us whether small heating events contribute substantially to the heating or not. In this work we show a link between the power law index and the operating heating mechanism in a loop. We set up two coronal loop models: in the first model Alfvén waves created by footpoint shuffling nonlinearly convert to longitudinal modes which dissipate their energy through shocks; in the second model numerous heating events with nanoflare-like energies are input randomly along the loop, either distributed uniformly or concentrated at the footpoints. Both models are based on a 1.5-D MHD code. The obtained coronae differ in many aspects, for instance, in the simulated intensity profile that Hinode/XRT would observe. The intensity histograms display power law distributions whose indexes differ considerably. This number is found to be related to the distribution of the shocks along the loop. We thus test the observational signatures of the power law index as a diagnostic tool for the above heating mechanisms and the influence of the location of nanoflares.

From the central limit theorem to heavy-tailed distributions

2003 ◽  
Vol 40 (3) ◽  
pp. 803-806 ◽  
Author(s):  
Jinwen Chen
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Power Law ◽  
Power Law Distribution ◽  
The Central Limit Theorem ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Random Indices ◽  
Power Law Distributions

It has been observed that in many practical situations randomly stopped products of random variables have power law distributions. In this note we show that, in order for such a product to have a power law distribution, the only random indices are the exponentially distributed ones. We also consider a more general problem, which is closely related to problems concerning transformation from the central limit theorem to heavy-tailed distributions.

Power Law Distributions and the Size Distribution of Strikes

2017 ◽  
Vol 48 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Michele Campolieti
Keyword(s):  
Size Distribution ◽  
Power Law ◽  
Model Fit ◽  
Power Law Distribution ◽  
Policy Perspective ◽  
Methodological Research ◽  
Canadian Data ◽  
Alternative Measures ◽  
Power Law Distributions ◽  
Research And Policy

Using Canadian data from 1976 to 2014, I study the size distribution of strikes with three alternative measures of strike size: the number of workers on strike, strike duration in calendar days, and the number of person calendar days lost to a strike. I use a maximum likelihood framework that provides a way to estimate distributions, evaluate model fit, and also test against alternative distributions. I consider a few theories that can create power law distributions in strike size, such as the joint costs model that posits strike size is inversely proportional to dispute costs. I find that the power law distribution fits the data for the number of lost person calendar days relatively well and is also more appropriate than the lognormal distribution. I also discuss the implications of my findings from a methodological, research, and policy perspective.

Effect of landslides on the structural characteristics of land-cover based on complex networks

2017 ◽  
Vol 31 (22) ◽  
pp. 1750156 ◽  
Author(s):  
Jing He ◽  
Chuan Tang ◽  
Gang Liu ◽  
Weile Li
Keyword(s):  
Land Cover ◽  
Complex Networks ◽  
Power Law ◽  
Satellite Images ◽  
Structural Characteristics ◽  
Power Law Distribution ◽  
Graph Topology ◽  
Linear Coefficient ◽  
Area Distribution ◽  
Before And After

Landslides have been widely studied by geologists. However, previous studies mainly focused on the formation of landslides and never considered the effect of landslides on the structural characteristics of land-cover. Here we define the modeling of the graph topology for the land-cover, using the satellite images of the earth’s surface before and after the earthquake. We find that the land-cover network satisfies the power-law distribution, whether the land-cover contains landslides or not. However, landslides may change some parameters or measures of the structural characteristics of land-cover. The results show that the linear coefficient, modularity and area distribution are all changed after the occurence of landslides, which means the structural characteristics of the land-cover are changed.

A Small-World Model of Scale-Free Networks: Features and Verifications

2011 ◽  
Vol 50-51 ◽  
pp. 166-170 ◽  
Author(s):  
Wen Jun Xiao ◽  
Shi Zhong Jiang ◽  
Guan Rong Chen
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Small World ◽  
Static Condition ◽  
Vertex Degree ◽  
Power Law Distribution ◽  
Least Common Multiple ◽  
Scale Free ◽  
Vertex Degrees

It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent  2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.

An analysis of power law distributions and tipping points during the global financial crisis

2018 ◽  
Vol 13 (1) ◽  
pp. 80-91 ◽  
Author(s):  
Yifei Li ◽  
Lei Shi ◽  
Neil Allan ◽  
John Evans
Keyword(s):  
Financial Crisis ◽  
Power Law ◽  
Global Financial Crisis ◽  
Operational Risk ◽  
Tipping Point ◽  
Power Law Distribution ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
The Global Financial Crisis ◽  
Power Law Distributions

AbstractHeavy-tailed distributions have been observed for various financial risks and papers have observed that these heavy-tailed distributions are power law distributions. The breakdown of a power law distribution is also seen as an indicator of a tipping point being reached and a system then moves from stability through instability to a new equilibrium. In this paper, we analyse the distribution of operational risk losses in US banks, credit defaults in US corporates and market risk events in the US during the global financial crisis (GFC). We conclude that market risk and credit risk do not follow a power law distribution, and even though operational risk follows a power law distribution, there is a better distribution fit for operational risk. We also conclude that whilst there is evidence that credit defaults and market risks did reach a tipping point, operational risk losses did not. We conclude that the government intervention in the banking system during the GFC was a possible cause of banks avoiding a tipping point.

Comparing Three Environmental Particle Size Distributions: Power Law (FED-STD-209D), Lognormal, Approximate Lognormal (MIL-STD-1246B)

1991 ◽  
Vol 34 (1) ◽  
pp. 21-24
Author(s):  
Douglas Cooper
Keyword(s):  
Particle Size ◽  
Power Law ◽  
Lognormal Distribution ◽  
Cumulative Distribution ◽  
Size Distributions ◽  
Power Law Distribution ◽  
Particle Size Distributions ◽  
Contamination Control ◽  
Control Programs ◽  
Power Law Distributions

Particle size strongly influences particle behavior. To summarize the distribution of particle sizes, a distribution function can be used. The characteristics of the particle size distributions chosen are important for two specification documents currently under revision: (1) FED-STD-209D, concerning air-cleanliness in manufacturing, which uses cumulative particle size distributions that are linear when plotted on log-log axes; these are power law distributions. (2) MIL-STD-1246B, "Product Cleanliness Levels and Contamination Control Programs," primarily concerning surface cleanliness, which uses cumulative particle size distributions that are linear when plotted as the logarithm of the cumulative distribution versus the square of the logarithm of the particle size, log2x, A third distribution, the lognormal, is commonly found in aerosol science, especially where there is a single particle source. The distributions are compared and discussed. The FED-STD-209D power law distribution can approximate a lognormal distribution over only a limited size range. The MIL-STD-1246B distribution is an asymptotic approximation to the lognormal distribution.

Dynamic Analysis of Human Behavior Based on User Log of ACM

2014 ◽  
Vol 998-999 ◽  
pp. 1570-1575
Author(s):  
Zi Yuan Long ◽  
Xu Han ◽  
Wen Jun Wang
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Human Behavior ◽  
Power Law ◽  
Specific Interaction ◽  
Behavioral Characteristics ◽  
Natural Phenomena ◽  
Power Law Distribution ◽  
Specific Factors ◽  
Previous Wording

Human behavior is one kind of complicated phenomena. Comprehensive and profound understanding of their behavioral characteristics has been the direction of the tireless efforts of people. In recent years, studies have shown that: if the time series of human behavior is a Poisson process, its probability distribution is exponential distribution interval. However, currently a number of empirical analyses show that: some of the probability distribution of the interval of events triggered by human behavior are Power-law distribution and the process is an intermittency process. In this paper, based on a statistical analysis of about 1300000 user log of TJU-ACM from 2004 to 2013, we found that distribution of the interval of submit time of users follows a power law with an exponent characteristic, which is a difference from the analysis results of the previous wording. After investigation, we knew the reason for this result is that the answer to the question of ACM online is driven by a specific interaction of interest. It also further demonstrates that for the time series of some natural phenomena and human behavior, its time domain features are shown a strong episodic, and its distribution characteristics are driven by specific factors.

VISIBILITY GRAPHS FOR TIME SERIES CONTAINING DIFFERENT COMPONENTS

2011 ◽  
Vol 10 (04) ◽  
pp. 371-379 ◽  
Author(s):  
JINGCHAO QI ◽  
JIANYONG WANG ◽  
JIANBO WANG ◽  
QIN XIAO ◽  
HUIJIE YANG
Keyword(s):  
Time Series ◽  
Power Law ◽  
Real World ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
Visibility Graphs ◽  
Hurst Exponents

We consider the visibility graphs for superpositions of fractional Brownian motions with different Hurst exponents. It is found that the degree distributions obey power-law. The components with lower Hurst exponents dominate the heterogeneity behaviors of the visibility graphs. These findings are helpful for us to understand the characteristics of visibility graphs for real-world time series.

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