The Poisson distribution

Introduction to Statistics in R

Maggie Matsui

Content Developer, DataCamp

Poisson processes

Events appear to happen at a certain rate, but completely at random
Examples
- Number of animals adopted from an animal shelter per week
- Number of people arriving at a restaurant per hour
- Number of earthquakes in California per year

Dog in animal shelter with family

Probability of some # of events occurring over a fixed period of time
Examples
- Probability of $\ge$ 5 animals adopted from an animal shelter per week
- Probability of 12 people arriving at a restaurant per hour
- Probability of $\lt$ 20 earthquakes in California per year

$\lambda$ = average number of events per time interval
- Average number of adoptions per week = 8

Poisson distribution with lambda = 8

3 Poisson distributions: one with lambda = 1, one with lambda = 5, and one with lambda = 8

If the average number of adoptions per week is 8, what is $P(\text{\# adoptions in a week} = 5)$?

dpois(5, lambda = 8)

0.09160366

If the average number of adoptions per week is 8, what is $P(\text{\# adoptions in a week} \le 5)$?

ppois(5, lambda = 8)

0.1912361

If the average number of adoptions per week is 8, what is $P(\text{\# adoptions in a week} \gt 5)$?

ppois(5, lambda = 8, lower.tail = FALSE)

0.8087639

If the average number of adoptions per week is 10, what is $P(\text{\# adoptions in a week} \gt 5)$?

ppois(5, lambda = 10, lower.tail = FALSE)

0.932914

rpois(10, lambda = 8)

13  6 11  7 10  8  7  3  7  6

Distribution of sample means from Poisson distribution with lambda = 8. Resembles the normal distribution

Introduction to Statistics in R