Brittle power: On Roman Emperors and exponential lengths of rule

On distribution-free goodness-of-fit testing of exponentiality

“…However, the value of the Kolmogorov-Smirnov statistic from the transformed empirical process is equal to d n ¼ 2:46, which corresponds to a p-value of 0:028. Hence the hypothesis of exponentiality should be rejected, which agrees with the more detailed analysis reported in Khmaladze et al (2007).…”

Efficiency of exponentiality tests based on a special property of exponential distribution

“…This is sustained by their high local Bahadur efficiency and considerable power under common alternatives. Our tests were able to reject the exponentiality of the sample of reigns of Roman emperors which was claimed by Khmaladze and his coauthors in [10], [19], [20]. We hope that our tests will be useful in other delicate cases when one has to confirm the rejection of exponentiality hypothesis.…”

“…Namely, as an application of new exponentiality tests, we examine the interesting question on the durations of reigns for Roman emperors discussed by Khmaladze and his coauthors [19], [20]. Our tests firmly reject the hypothesis of exponentiality, and this contradicts the findings of Khmaladze and his team, see also [9] and [38].…”

“…In these papers the authors came to the surprising agreement of data with the exponential distribution. However, they used only one test for exponentiality of Kolmogorov type proposed by Haywood and Khmaladze [10], [19], [20]. This test is probably not sensitive enough, and the single agreement with the exponentiality stated by these authors does not convince us in the validity of H 0 .…”

“…The chronology shows the dates of ascent and abdication (or death). In the cases where exist no specific day of month we select a mid-points as it was done in [20] and [19]. In these papers the authors came to the surprising agreement of data with the exponential distribution.…”