# Poisson distribution

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Published on October 7, 2008

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Poisson : Poisson headlessprofessor When to use? : When to use? Variable is measured on discrete ratio scale When to use? : When to use? Variable is measured on discrete ratio scale Examples: events, accidents, absences, defects, complaints When to use? : When to use? Variable is measured on discrete ratio scale Events independent When to use? : When to use? Variable is measured on discrete ratio scale Events independent Sample space is not cases, but time period, length, area or volume Example : Example How many industrial accidents are there in a one month period? Example : Example How many traffic accidents are there in a ten mile length of road? Example : Example How many production defects are there in a thousand yards of cloth? Example : Example How many dust particles are there in a 100,000 liter room? Poisson chart : Poisson chart Rows represent how many events observed X Poisson chart : Poisson chart Rows represent how many events observed X Must be a whole number Poisson chart : Poisson chart Rows represent how many events observed X Columns represent expected frequency Poisson chart : Poisson chart Rows represent how many events observed X Columns represent expected frequency: such as a population mean or other norm Poisson chart : Poisson chart Rows represent how many events observed X Columns represent expected frequency: such as a population mean or other norm, which may be a decimal number Poisson chart : Poisson chart Rows represent how many events observed X Columns represent expected frequency Distribution has left truncation & right skew Example : Example What is the probability of having no accidents in a week when the average is .2? Example : Example What is the probability of having no accidents in a week when the average is .2? The observed frequency X row would be 0. Example : Example What is the probability of having no accidents in a week when the average is .2? The observed frequency X row would be 0. The expected column would be .2 Example : Example What is the probability of having at least one accident in a week when the average is .2? Answer : Answer P = .18 Answer : Answer P = 1.00 - .82 P = .18 Example : Example What is the probability of having exactly three accidents in a week when the average is .1? Example : Example What is the probability of having exactly three accidents in a week when the average is .1? The observed frequency X row would be 3. Example : Example What is the probability of having exactly three accidents in a week when the average is .1? The observed frequency X row would be 3. The expected column would be .1 When the time period is longer : When the time period is longer Multiply the expected frequency Poisson tables : Poisson tables Go up to an expected frequency of 5.0 Poisson tables : Poisson tables Go up to an expected frequency of 5.0 Above that, consider using a normal curve approximation Poisson tables : Poisson tables Go up to an expected frequency of 5.0 Above that, consider using a normal curve approximation or a Chi Square for expected and observed frequencies What does it prove? : What does it prove? If you get an extremely low probability, that merely means that your observed results are unlikely to conform to the frequencies expected by the Poisson distribution. Poisson : Poisson headlessprofessor

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