Rare events are, well, very rare, and this can make it difficult to know how likely they are to occur in any given time frame. Statisticians must look at a large enough body of data to make any useful prediction about it. But how do you find a large enough sample of events that donıt happen very often?
Fortunately, mathematicians have a useful tool to do this: the Poisson distribution, also known as the "law of large numbers."
The Poisson distribution describes the probability that a random, rare event will occur in a given interval of time, such as the number of no-hitters occurring over and entire 162-game baseball season. While the probability of the event occurring is very small, the number of opportunities for it to happen is so large that the event actually occurs a few times. The longer the time interval, the more the data begins provide a pattern from which predictions can be made.
The Poisson distribution is particularly useful in the study of how diseases spread through populations, called epidemiology. For instance, letıs say that we know that in any given population of 10,000 people exposed to a certain disease, 10 will actually develop it. If 14 people actually contracted the disease, this would not be ıstatistically significant,ı because it falls within the error rate. But if 200 people got the disease, this would be far above the so-called standard deviation.
The Poisson distribution can be used to determine birth defect probabilities; the number of sample defects on a car; the number of typographical errors on a printed page; or the number of insect parts likely to be found in a chocolate bar.
The American Mathematical Society contributed to the information found in the TV portion of this report.