Law of small numbers
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The law of small numbers may refer to
- the Poisson distribution. Sometimes probability distributions are called laws, and the use of that name for this distribution originated in Ladislaus Bortkiewicz's book The Law of Small Numbers;
- Bortkiewicz's book mentioned above;
- the tendency for an initial segment of data to show some bias that drops out later (one example in number theory being the Kummer's conjecture on cubic Gauss sums);
- the occurrence of mathematical coincidences that are no more than some expression of a pigeonhole principle. Richard Guy has written on topics of this kind;
- the tendency to extrapolate big conclusions from small samples. An example would be sports fans assuming that a few excellent performances are proof of a player’s underlying ability. Another example would be investors, who may assume that a mutual fund’s record over one year is a reliable indicator of the manager’s skill.
- In order for a sequence to be considered representative, people think that every segment of a random sequence should reflect the true proportion.
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