the.com/poisson
the probability distribution for things that rarely happen but keep happening anyway.
means a formula that predicts how many times a rare, random event will occur in a fixed span of time or space, given only its average rate.
from named after siméon denis poisson, a french mathematician who derived it in 1838 while working out approximations to the binomial distribution for rare events, in a book about the judicial process and probability.
one parameterneeds only the average rate, called lambda
mean equals varianceboth are exactly lambda, always
discrete counts onlymodels 0, 1, 2 events, never fractions
limit of binomialemerges when trials rise, success rate shrinks
for instance
prussian cavalry deaths — ladislaus bortkiewicz used it on horse-kick fatalities, 1898
call center staffing — predicts hourly call volume to size phone teams
radioactive decay counts — geiger counter clicks per minute follow it closely
typo counts per page — editors estimate errors using the same math