Celebrities die 2.7183 at a time
The claim that celebrities die in threes is usually dismissed as the result of the human propensity to see patterns where there are none. But celebrities don’t die at regularly spaced intervals either. It would be very weird if a celebrity predictably died on the 14th of every month. And once you deviate from a regularly spaced pattern, some amount of clustering is inevitable. Can we make this more precise?
Rather than trying to define exactly what constitutes a celebrity, I’ll simply assume that they die at a fixed rate and that they do so independently of each other (The Day the Music Died notwithstanding). It follows that celebrity deaths is a Poisson process with intensity $\lambda$ where $\lambda$ is the number of deaths that occur in some fixed time period.
As an example, suppose we define celebrityhood in such a way that twelve celebrities die each year on average. Then $\lambda = 12/\text{year}$, and because the time between events in a Poisson process is exponentially distributed with parameter $\lambda$, the average time between two deaths is $1/\lambda$ = 1/12th year, or one month.
