Shark Attacks May Be A "Poisson Burst"

"It really does seem that there is indeed something odd going on with the ocean currents, temperatures, food supply, or water chemistry, which would explain the recent reported spate of shark attacks; however, even if such attacks were purely 'random' and independent of each other, it is not surprising that they seem to occur in 'clumps' in time--like this past summer-- and then not at all for a long time," explains David Kelton, professor of management science in Penn State's Smeal College of Business.

Kelton, who researches the probabilistic and statistical aspects of simulation, is chair of Smeal College's Department of Management Science and Information Systems.

"There is something in probability theory called a Poisson process, giving amazingly good descriptions of such random independent events occurring through time, like customer arrivals to a fast-food store, cosmic rays striking a planet, accidents in a factory, airplane mishaps, and maybe shark attacks," says Kelton.

Reasonable and realistic physical assumptions imply that the time between successive events follows what is called an exponential distribution, the most likely value of which is zero (or arbitrarily close to zero).

"So on a time line, you see lots of very small inter-event times, meaning that the events happen in clumps, then a long time will go by when nothing happens, representing an infrequent but possible observation from the right tail of the distribution," says Kelton. "After the fact, it seems that 'it never rains but what it pours.' This is what's sometimes called a 'Poisson burst' of events."

This process, Kelton points out, was discovered by the French mathematician and probabilist Poisson, who was consulting with the Prussian army to explain why so may Prussian army officers were being killed by getting kicked by horses.