News Stories about Shark Attacks in Hawaii
(Dec. 12, 2013)
Some newspapers in Hawaii are reporting that, until recently, there are
about 4 attacks per year of sharks on humans. In 2013, there have
been 13 attacks so far. The writers of these stories think
"something has changed", and then go on to discuss what and how to
If one assumes that rare events, like shark attacks, follow a Poissson
distribution, the mean number of attacks is the same as the parameter
Lamda of the distribution. Specifically, having a Poisson
distribution with parameter Lambda means here that the probability
of exactly K attacks in a year is then Exp(-Lambda) (Lambda^K)/(K!).
With the assumption that Lambda = 4 for shark attacks in Hawaii, having
13 shark attacks or more has probability of
0.000273717 (or about 3 chances in 10,000). So, each person has
a choice: believe that 2013 is very unlucky year, or that the
historical pattern of 4 shark attacks per year no longer is true.