Statistical properties of user activity fluctuations in virtual worlds

Abstract

User activity fluctuations reflect the performance of online society. We investigate the statistical properties of 1-min user activity time series of simultaneously online users inhabited in 95 independent virtual worlds. The number of online users exhibits clear intraday and weekly patterns due to human's circadian rhythms and week cycles. Statistical analysis shows that the distribution of absolute activity fluctuations has a power-law tail for 44 virtual worlds with an average tail exponent close to 2.15. The partition function approach unveils that the absolute activity fluctuations possess multifractal features for all the 95 virtual worlds. For the sample of 44 virtual worlds with power-law tailed distributions of the absolute activity fluctuations, the width of singularity $\Delta \alpha$ is negatively correlated with the maximum activity ($p$-value=0.070) and the time to the maximum activity ($p$-value=0.010). The negative correlations are not observed for neither the other 51 virtual worlds nor the whole sample of the 95 virtual worlds. In addition, numerical experiments indicate that both temporal structure and large fluctuations have influence on the multifractal spectrum. We also find that the temporal structure has stronger impact on the singularity width than large fluctuations.

arXiv comment9 pages including 8 figures

References in corpus (25)

• Power-law distributions in empirical data
• Multifractal detrended fluctuation analysis of nonstationary time series
• The origin of bursts and heavy tails in human dynamics
• Improved surrogate data for nonlinearity tests
• Surrogate time series
• Detrending moving average algorithm for multifractals
• The components of empirical multifractality in financial returns
• On Universality in Human Correspondence Activity
• Calling patterns in human communication dynamics
• Circadian pattern and burstiness in mobile phone communication
• Finite-size effect and the components of multifractality in financial volatility
• Multifractal analysis of Chinese stock volatilities based on partition function approach
• Multifractality in stock indexes: Fact or fiction?
• A Multifractal Analysis of Asian Foreign Exchange Markets
• Joint multifractal analysis based on the partition function approach: Analytical analysis, numerical simulation and empirical application
• Division of labor, skill complementarity, and heterophily in socioeconomic networks
• Scale invariant multiplier and multifractality of absolute returns in stock markets
• Liquidity and the multiscaling properties of the volume traded on the stock market
• Endogenous and exogenous dynamics in the fluctuations of capital fluxes: An empirical analysis of the Chinese stock market
• Scaling and memory in recurrence intervals of Internet traffic
• Multiplier phenomenology in random multiplicative cascade processes
• Online-offline activities and game-playing behaviors of avatars in a massive multiplayer online role-playing game
• Two-state Markov-chain Poisson nature of individual cellphone call statistics
• Experimental evidence for the interplay between individual wealth and transaction network
• Statistical properties of online avatar numbers in a massive multiplayer online role-playing game

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