The Poisson distribution is a probability distribution that models the probability that a certain number of events will occur during a specific time period. Baron Simeon Denis Poisson, French mathematician, originally derived the Poisson distribution in 1830. He developed the distribution to describe the number of times a gambler would win in difficult game of chance in a large number of tries.

Data professionals use the Poisson distribution to model data, such as the expected number of visitors per hour for a website, the expected number of calls per hour for a customer service call center, customers per day at a restaurant, and thunder storms per month in a city. Other types of data would be number of imperfections in a square meter of fabric or number of typos per product entered into a computer inventory system. We look at the mean number of events that occurs in a specified interval of time or space.

The Poisson distribution represents a type of random experiment called a Poisson experiment. A Poisson experiment has the following attributes.

• The number of events in the experiment can be counted
• The mean number of events that occurred during a specific time period is known
• Each event is independent

For example, we could generate random numbers from a Poisson distribution For example, if incoming service calls average two per minute, our Poisson distribution will simulate 100 minutes, returning the number of calls in each of those 100 minutes.

Below is the formula.

In the above formula, the Greek letter lamda is the mean number of events that occur in a specific time period. k refers to the number of events. e is a constant that is approximately 2.71828. The exclamation point stands for factorial.

Retail Orders per Minute

Let’s consider a drive through at a restaurant. the drive-through service at a restaurant receives an average of two orders per minute. We can calculate the probability that the drive through receives zero, 1, 2, or 3 orders per minute. After plugging in these numbers into the formula, you can then create a histogram showing our results.