Poisson Distribution- Use Cases and Examples (Data Science)
Poisson distribution is one of the most widely used probability distributions in data science.
The Poisson distribution is a way to understand how often rare events happen randomly over time or space. In this blog, we will explore the Poisson distribution and its properties.
It is named after French mathematician Simeon-Denis Poisson, who first introduced it in 1837.
We typically use Poisson distribution when we want to measure the number of events per unit of time.
USE CASE
Let’s say you have Capacity planning at a call center
It means at any call center, we need call center representatives to receive customer calls or it could be an emergency center from people who are in distress, they need to take some actions or services to dispatch.
Capacity planning here means how many people we need at the call center looking at distributions of calls that we have been receiving in the past.
EXAMPLE 1.
Number of calls you get at call-center
What is happening here?
Getting a call, the call is an event, unit time is like 1 hour.
so we are trying to get or study the number of calls per unit of time.
EXAMPLE 2.
Go to the Amul cafe in your university and see how many people are coming there every 10 minutes.
so again this is also a number of events that are happening for a unit of time.
EXAMPLE 3.
When you have a cell tower:
How many calls arrive at the cell tower per unit of time?You have to understand how many events or phone calls you will have to receive at the cell tower because it will help you determine how many cells tower you have to place in a specific region.
But when we apply Poisson distribution, there are a bunch of necessary conditions that have to be satisfied when you are using Poisson distribution.
CONDITIONS
- Events should happen at a constant rate (λ)
In the real world if it does not happen at exactly a constant rate if it is approximately at a constant rate it is good enough.
2. Events are independent
Calls that you are getting at a call center, me making a call to call centers is independent of you making calls to call centers.
3. No Simultaneous events
MATHEMATICS ASSOCIATED
It is a discrete random variable, so we will have PMF (Probability Mass Function)
Why it is Discrete?
Because the number of calls can be 4, 5, 6
but cannot be 4.5, 4.6
It arrived in two ways:
- Derive Mathematically: We can derive using binomial distributions and using limits in calculus.
- By fitting a formula to observations.
What Poisson Says is?
What is the probability that you will see K events
K is the number of events that are happening
λ is the rate at which these events are happening.
X is nothing but count.