New Zealand Statistical Association

NZSA 2009

Victoria University of Wellington

John Haywood

Victoria University of Wellington

Here today, gone tomorrow? Exponential reign lengths revealed and explained

This is joint work with Estate Khmaladze and Ray Brownrigg, both VUW

Human lifetimes have an increasing failure rate, or force of mortality; as people age they are more likely to die. We consider the succession of Chinese Emperors from 221 BCE to 1911 CE and show that, unlike lifetimes, their reigns ceased at a constant rate, unaffected by elapsed time or by accumulated social, political or economic tensions. Reign lengths of the 'Sons of Heaven' followed the same memoryless exponential distribution for over two millennia; the 'half-life' of an emperors' reign was 10 years. Thus becoming emperor influenced the duration of remaining life and, surprisingly, length of rule was independent of age at ascent.

To test for exponentiality of reign lengths we use a distribution-free goodness-of-fit test applied to a transformed empirical process, with non-trivial power against alternatives of any type. We also use two tests specifically targeted at an alternative explanation of a mixture of remaining life distributions. Building on certain asymptotic results in the theory of stochastic processes, we propose an explanation of the observed exponential reign lengths, with fundamental implications for the nature of rule: even stable and civilised societies, like Imperial China, do not require nor imply stability of their ruler.
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