What exactly is Poisson Distribution in data analysis?

Introduction to Poisson Distribution

Named after the French mathematician, Simeon Denis Poisson, the Poisson Distribution provides a framework which models the likelihood of events occurring within a fixed interval of time. For example, how many deaths could occur as the result of a particular illness in a city, what is the likelihood of a flood, bushfire, earthquake or other natural disaster, calls expected at a call centre, number of car accidents at a certain intersection or waiting times between events.

Understanding the Poisson Distribution formula

Unless you’re familiar with formulas, calculating Poisson Distribution could be a tad confusing. Let’s break it down for some clarity.

The formula is:

P(x; λ) = (e^(-λ) * λ^x) / x!

 Where:

P = probability

x = events occurring within the interval of time

λ = the average rate of events happening per unit of time or space

Poisson Distribution vs. Normal Distribution

Essentially, normal distribution assumes a symmetric pattern, whereas Poisson Distribution focuses on count data (such as the number of occurrences of something). Normal distribution is also known as the Guassian distribution, which is suitable for continuous data and characterised by its bell-shaped curve, whereas Poisson is used for discrete data and describes the probability of events occurring at very specific points, within a set time frame.

Examples of Poisson Distribution in real life

We’ve already touched on a few Poisson Distribution examples of where the model might be applied, but let’s get further details on some typical scenarios.

Network traffic

Gaining an understanding of the patterns of computer network traffic is possible with the Poisson Distribution as the number of data packets arriving at a network router during specific times can be predicted. This kind of data is important for optimising networks and capacity planning, particularly for organisations with ongoing large volumes of data traffic.

Insurance claims

Ah, good old insurance. It might not come as a complete shock to learn that the Poisson Distribution is applied by insurance companies to estimate the number of claims they can expect within a given timeframe. This might even be drilled down into specific types of claims. The results are then used to calculate premiums and manage risks.

Infection rates

A more recent example where Poisson distribution could well and truly have been applied is the Covid-19 global pandemic. Applying the Poisson Distribution could have revealed the probability of outbreak within a set time frame within any given community or region. Covid aside, this approach could also predict the evolution and global spread of any infectious disease.

Call centre analysis

Applying Poisson Distribution in a call centre setting can assist with analysing the number of incoming calls within a specific time frame and support the prediction of call volumes. Being armed with this data can enable management to recruit, source and allocate the appropriate amount of resources, including staffing, to ensure the maximum number of calls can be covered. This could apply to any call centre, but is vital to centres that take calls for emergencies and then dispatch the relevant support throughout communities.

How to calculate Poisson Distribution using Excel

If you want to calculate the probability of a specific number of events, you can turn to good old Excel and follow the four steps below. This simple Excel function enables you to easily calculate Poisson Distribution probabilities and saves you some time with your data analysis.

1. Open Excel and enter your desired values into separate cells for λ (average rate) and x (the number of events).
2. In a new cell, use the formula “=POISSON.DIST(x,λ,FALSE)” to calculate the Poisson Distribution probability. The FALSE argument indicates that you want the exact probability rather than an approximation.
3. Replace “x” and “λ” in the formula with the corresponding cell references in your Excel spreadsheet.
4. Press Enter to get the probability value.