The Poisson distribution is a discrete probability distribution, so it can be described by a probability mass function and cumulative distribution function.

We can use the poisson.pmf() method in the scipy.stats library to evaluate the probability of observing a specific number given the parameter (expected value) of a distribution. For example, suppose that we expect it to rain 10 times in the next 30 days. The number of times it rains in the next 30 days is “Poisson distributed” with lambda = 10. We can calculate the probability of exactly 6 times of rain as follows:

import scipy.stats as stats
# expected value = 10, probability of observing 6
stats.poisson.pmf(6, 10)

Output:

0.06305545800345125

Like previous probability mass functions of discrete random variables, individual probabilities can be summed together to find the probability of observing a value in a range.

For example, if we expect it to rain 10 times in the next 30 days, the number of times it rains in the next 30 days is “Poisson distributed” with lambda = 10. We can calculate the probability of 12-14 times of rain as follows:

import scipy.stats as stats
# expected value = 10, probability of observing 12-14
stats.poisson.pmf(12, 10) + stats.poisson.pmf(13, 10) + stats.poisson.pmf(14, 10)

Output:

0.21976538076223123