Here's an analysis I'm sending to the staff writer of the three recent dog biting incidents in Salinas Am I all wet, or is it cogent? -- before I send it off, your critique.
bc
People!
Animal control officers characterize the three pit bull attacks in Salinas* on the same day as a statistical anomaly. This is not true! That it is a rare event is simply because pit bull attacks are rare, especially if in a small area, e.g. a city.
Dog attacks are random, because there are many factors that cause an attack. Therefore, the central limit theorem applies.** Because the number of attacks is infrequent, the possibility of attack is high (very frequent dog person interactions), and they are random and unrelated, the Poisson distribution applies. A corollary of that distribution is the Poisson interval process,*** which is, the interval between events is an exponential function, i.e. the number of events increases exponentially with decreasing time interval. (time between the events)
A common method of determining, if infrequent, but very possible (not probable) events observe the Poisson distribution is to plot the event number in each of increasing intervals. This is, for example, a method used to test the functioning of a nuclear radiation detector using a radioactive source.
To test that dog bites observe a Poisson distribution, and show the dog bite animal Salinas events were not anomalous, I analyzed the data of dog bite fatalities**** over the three years 2009=>2011 as reported by the media in the US. Because there were about 75 fatalities in the three year period, I grouped the data in successive seven day intervals. The plot is here:
The time interval between fatalities:
Fatal dog attacks 3 years seven day intervals.tiff 1,168×738 pixels
bc forgot all three attacked were animals, tho in one case the dog threatened an officer, hence this makes multiple same day in the same city attacks even more likely! And he reads the newspaper.
**** I didn't find by Googling quickly just dog attacks, so I used the fatality data. (next URL) I suspect only a small proportion of attacks result in death, and since several fatalities occurred on the same day, it's not very unlikely that multiple attacks would occur in the same city on the same day.
List of fatal dog attacks in the United States - Wikipedia, the free encyclopedia