Part 1. Goodness of fit testing of exponentiality: a special case of some general approach.

Part 2. "Application to historical demography: reign times of Emperors and Kings".

In Part 1 we present the form of asymptotically distribution free version of empirical process, which, under hypothesis of exponentiality, converges to standard Brownian motion. Our aim is to show that the form of this process is very simple, and that its convergence to the limit is quick. We will also discuss strange irregularities in the literature on goodness of fit testing of exponentiality.

Biological objects and certainly human beings can not have exponentially distributed life-times, unless the death is caused by an accident. In Part 2 we show that the duration of reigns of Roman Emperors follows, nonetheless, exponential distribution. In search of the counter example we studied duration of reign of Chinese Emperors throughout the span of their enormous history. But these durations also follow exponential distribution. We compare possible explanations, and then present the counter example in the duration of reign of European monarchs after Medieval times.