On the mathematical lifetime mechanism of Chinese dynasties

Abstract The long history of China is composed of different imperial dynasties. However, all dynasties only survive limited time and follow the identical development process, which is a dynamical process from establishment to extinction. Based on the historical fact about the Chinese dynasties, this paper proposes a continuous-time Markov chain model combined with Coxian phase-type distributions to investigate the survival time for Chinese dynasties. Our model includes four different states, which correspond to the four typical social and political states for the traditional Chinese imperial dynasties. Three states are transient, which are the establishment state, the prosperity state, the rottenness state, and one state is absorbing, which is the perishment state. We use the historical survival time data for Chinese dynasties to estimate our model by maximizing the log-likelihood function. We obtain the closed-forms for the transition probabilities, the survival function and the force of mortality for Chinese dynasties. The analysis for hitting times and absorption probabilities shows that Chinese dynasties can survive 92 years on average. We use our model to conduct the phases analysis, which can be used to predict the current social state given the excising survival years for Chinese dynasties. Based on our analysis, we give suggestions on foreign policy and business.