Original question (7/25/14): Does this quotation from the news media make sense, or is there a better statistical way of viewing the spate of recent plane accidents?
However, Barnett also draws attention to the theory of Poisson distribution, which implies that short intervals between crashes are actually more probable than long ones.
"Suppose that there is an average of one fatal accident per year, meaning that the chance of a crash on any given day is one in 365," says Barnett. "If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August."
"It seems counterintuitive, but the conclusion follows relentlessly from the laws of probability," Barnett says.
Clarification (7/27/14): What is counter intuitive (to me) is saying that rare events tend to occur close in time. Intuitively, I would think that rare events would not occur close in time. Can anyone point me to a theoretical or empirical expected distribution of the time between events under the assumptions of a Poisson distribution? (That is, a histogram where the y-axis is frequency or probability and the x-axis is time between 2 consecutive occurrences grouped into days, weeks, months, or years, or the like.) Thanks.
Clarification (7/28/14): The headline implies it is more likely to have clusters of accidents than widely spaced accidents. Lets operationalize that. Let's say that a cluster is 3 airplane accidents, and a short period of time is 3 months and a long period of time is 3 years. It seems illogical to think that there is a higher probability that 3 accidents will occur within a period of 3 months than within a period of 3 years. Even if we take the first accident as a given, it is illogical to think that 2 more accidents will occur within the next 3 months as compared to within the next 3 years. If that is true, then the news media headline is misleading and incorrect. Am I missing something?