From heavy-tailed to exponential distribution of interevent time in cellphone top-up behavior

Abstract

Cellphone top-up is a kind of activities, to a great extent, driven by individual consumption rather than personal interest and this behavior should be stable in common sense. However, our researches find there are heavy-tails both in interevent time distribution and purchase frequency distribution at the global level. Moreover, we find both memories of interevent time and unit price series are negative, which is different from previous bursty activities. We divide individuals into five groups according to the purchase frequency and the average unit price respectively. Then, the group analysis shows some significant heterogeneity in this behavior. On one hand, we obtain only the individuals with high purchase frequency have the heavy-tailed nature in interevent time distribution. On the contrary, the negative memory is only caused by low purchase-frequency individuals without burstiness. On the other hand, the individuals with different preferential price also have different power-law exponents at the group level and there is no data collapse after rescaling between these distributions. Our findings produce the evidence for the significant heterogeneity of human activity in many aspects.