Here we investigate Tianya Forum (a worldwide influential Chinese network community) users behaviors patterns (such as posting, clicking stream, and posts survival rule etc). We provide probabilistic models to describe the frequencies of Blog Users clicking and replying behaviors. From both stochastic modeling and psychophysical (sensation-stimulus) explanation aspects, we found 

    (1) the ratio between clicking and replying volume satisfies relation of power function. To explain this phenomenon, we relate the Weber-Fechner and Stevens  laws of psychophysics to explain how replying behavior is quantitatively manifested in the online response of a large number of individuals’ collective clicking stimulus, which can be described by a power function.

    (2) the frequencies of Blog Users clicking volumes satisfies log-normal distribution, in addition, both the lower-tail and upper-tail demonstrate power-law behaviour. Based on Geometric Brown Motion (GBM), this article provided a quantitative interpretation for the collective phenomenon. We also analyzed the double tails patterns, which is verified empirically for clicking data.

    (3) both the frequencies of replying volumes ( which is introduced to account for the novelty decay) and the replying time interval satisfy exponential distribution. We also find that the survival period is subjected to the power-law distribution.

    (4) Finally, we found the exponential decay pattern of replying frequencies results in a linearly clicking volumes increasing at the first several hours, and then consecutively tend to a stable level, we also rigorously interpret the increasing pattern based on mathematic analysis.

    Bio:

    李振鹏,副教授,大理学院统计系主任