I am teaching stochastic processes again this semester. After enjoying a humorous exchange on twitter about the exponential distribution, I wondered about the practicality of the exponential distribution. Most of the examples from my notes seem a little idealized. For example, I’m almost positive that light bulb times are not exponentially distributed. Is anything really exponentially distributed?
Things that are almost certainly exponentially distributed:
- The amount of ink and graffiti on dollar bills that have been in circulation more than one year (a student who works for the Federal Reserve Bank provided this useful tifbit!).
- The useful life of things made from polyurethane foam, such as Nerf balls, car seats, mattress pads, and carpet pads (the useful life occurs after the break-in period and prior to the break-down period).
- The time between 911 calls (see below).
- The time between celebrity deaths.
I looked at some emergency medical 911 data. The call volume changes over the course of the day, but the call volume is constant for a large part of the day. Looking just at that time period, I examined the interarrival times of the 911 calls. The exponential distribution is more or less a perfect fit! I don’t have any data for my celebrity deaths hypothesis, but since they are independent, like most 911 calls, then I would expect celebrity deaths to follow an exponential distribution.
What else is exponentially distributed? Do you know how light bulb lifetimes are distributed?