Bitcoin transaction behavior modes exploration based on balance data

When analyzing the balance distribution of Bitcoin users, we found that it follows a log-normal pattern based on a rigorous Uniformly-Most-Powerful-Unbiased test. Drawing parallels from the successful application of Gibrat’s law in explaining city size and word frequency distributions, we tested whether a similar principle could account for the log-normal distribution in Bitcoin balances. However, our calculations revealed that the exponent parameters in both the drift and variance terms deviate slightly from 1 when applying Geometric-Brownian-Motion on the Bitcoin balance, which means that Bitcoin users’ balance distribution cannot be explained only by the proportional growth rule alone. During this exploration, Bitcoin users’ behaviors are also investigated. We discovered an intriguing phenomenon: Bitcoin users tend to fall into two distinct categories based on their transaction behavior, which we refer to as “poor” and “wealthy” users. Poor users who initially purchase only a small amount of Bitcoin tend to buy more Bitcoins first and then sell out all their holdings over time. The certainty of selling all their coins is higher and higher with time. In contrast, wealthy users who acquire a large amount of Bitcoin from the start tend to sell off their holdings over time. The speed at which they sell their Bitcoins is lower and lower over time. The wealthier the user, the larger the proportion of their balance and the higher the certainty they tend to sell their holdings. This research provided a new perspective to explore Bitcoin users’ behaviors which may apply to other finance markets.