Table of Contents
The dpois, ppois, qpois, and rpois functions in R are used to calculate the probability distribution of a Poisson random variable. The dpois function returns the probability density, the ppois function returns the cumulative probability, the qpois function returns the quantiles, and the rpois function returns random samples from the Poisson distribution.
This tutorial explains how to work with the in R using the following functions
- dpois: returns the value of the Poisson probability density function.
- ppois: returns the value of the Poisson cumulative density function.
- qpois: returns the value of the inverse Poisson cumulative density function.
- rpois: generates a vector of Poisson distributed random variables.
Here are some examples of cases where you might use each of these functions.
dpois
The dpois function finds the probability that a certain number of successes occur based on an average rate of success, using the following syntax:
dpois(x, lambda)
where:
- x: number of successes
- lambda: average rate of success
Here’s an example of when you might use this function in practice:
It is known that a certain website makes 10 sales per hour. In a given hour, what is the probability that the site makes exactly 8 sales?
dpois(x=8, lambda=10) #0.112599
The probability that the site makes exactly 8 sales is 0.112599.
ppois
The ppois function finds the probability that a certain number of successes or less occur based on an average rate of success, using the following syntax:
ppois(q, lambda)
where:
- q: number of successes
- lambda: average rate of success
It is known that a certain website makes 10 sales per hour. In a given hour, what is the probability that the site makes 8 sales or less?
ppois(q=8, lambda=10) #0.3328197
The probability that the site makes 8 sales or less in a given hour is 0.3328197.
It is known that a certain website makes 10 sales per hour. In a given hour, what is the probability that the site makes more than 8 sales?
1 - ppois(q=8, lambda=10) #0.6671803
The probability that the site makes more than 8 sales in a given hour is 0.6671803.
qpois
The qpois function finds the number of successes that corresponds to a certain percentile based on an average rate of success, using the following syntax:
qpois(p, lambda)
where:
- p: percentile
- lambda: average rate of success
Here’s an example of when you might use this function in practice:
It is known that a certain website makes 10 sales per hour. How many sales would the site need to make to be at the 90th percentile for sales in an hour?
qpois(p=.90, lambda=10)
#14
A site would need to make 14 sales to be at the 90th percentile for number of sales in an hour.
rpois
The rpois function generates a list of random variables that follow a Poisson distribution with a certain average rate of success, using the following syntax:
rpois(n, lambda)
where:
- n: number of random variables to generate
- lambda: average rate of success
Here’s an example of when you might use this function in practice:
Generate a list of 15 random variables that follow a Poisson distribution with a rate of success equal to 10.
rpois(n=15, lambda=10)
# [1] 13 8 8 20 8 10 8 10 13 10 12 8 10 10 6
Since these numbers are generated randomly, the rpois() function will produce different numbers each time. If you want to create a reproducible example, be sure to use the set.seed() command.