Understanding Poisson Distribution in Data Science

🍻 Hey, all you AI guys out there! Greetings from Berlin, the city that never sleeps... or runs out of bars, it seems!

we have covered some ground on probability and statistics already.

🚶♂️🚶♀️ Today, while walking down one of Berlin's bar-ing streets with a friend who's new in town, we played a little game I like to call "Guess the number of Bars" [it is not what you're thinking]. It's a nifty example of the Poisson distribution in action. Let's dive in.

Remember our Random Variables session? We talked about how they're the backbone of probability and statistics. Think of the number of bars as a random variable - it could be any number, but we use Poisson to make an educated guess.

What is Poisson Distribution (PD)? Poisson distribution is like that friend who is good at predicting things - except it is all about maths and probabilities. PD is used when you want to predict how many times something will happen in a set space or time. In our case, we're counting bars on a street in Berlin. Fun, right?

Poisson distribution falls into Discrete distribution which I explored here earlier.

Here was the scenario: We were walking in Berlin Street nd noticed about 10 bars every 500 meters. Then my friend asked, "How many bars are we gonna see in the next 250 meters?" Classic Poisson question, my friend!

Let's break it down:

1. Define the Problem: We've got 10 bars in every 500 meters.
2. Identify the Parameters: In PD, we have got a λ (lambda) - that's our average rate, which here is 10 bars per 500 meters.
3. Adjust λ for Our Distance: We were talking for 250 meters now, so let's halve 1/2 that rate. That makes sense, right? So, λ becomes 5 bars for 250 meters.
4. Crunch the Numbers: Here comes the fun part. We use this PMF formula:P(X = k) = (e^(-λ) * λ^k) / k! (This is our PMF for Poission, read about PMF here)This looks more complicated than choosing a drink at a Berlin bar, but stay with me!
5. Calculate for Different k Values: For 0 bars: P(X = 0) ≈ 0.67%. The chance of a bar desert!For 1 bar: P(X = 1) ≈ 3.37%. Getting warmer.For 2 bars: P(X = 2) ≈ 8.42%. Now we're talking!

So, what does this tell us? Well, it's like predicting how many times you'll regret your beer choice in a night.

💭 Here's a Thought: Ever wondered how often you will find a good bar when wandering in a new city say New York or Paris [Note - Poission was invented by French mathematician Simeon Denis Poisson, so you better know this when you go Paris]? Well, now you have got a tool to guesstimate that - all thanks to our buddy, Poisson!

➡️ More examples where Poisson distribution is happening

❓ Email Arrivals: Modeling the number of emails received per hour in an inbox.

❓ Insurance Claims: Analyzing the frequency of insurance claims filed in a month.

❓Phone Calls: Estimating the number of phone calls arriving at a call center in a given day.

❓Website Traffic: Predicting the number of website visits per hour.

❓Manufacturing Defects: Counting the number of defects per batch in a production process.

❓Arrival of Customers at a Store: Calculating the number of customers entering a store per hour.

❓Arrival of Buses at a Bus Stop: Modeling the number of buses arriving at a bus stop per hour.

❓Accidents at a Busy Intersection: Estimating the number of accidents occurring at a busy intersection per week.

❓Whatsup Message Arrivals: Analyzing the number of WhatsApp messages received per minute on a mobile device.

❓Medical Events: Predicting the number of medical emergencies at a hospital in a day.

Do you have any quirky scenarios where you think the Poisson distribution could come in handy? Share them in the comments! Or better yet, next time you're out and about, guess something using this method and tell me how it goes. Let's bring some fun into data science, one probability at a time!

Until next time, keep it nerdy and stay curious! 🤓 #datascience #poissondistribution #berlinbars #casualdatascience

P.S. - Stay tuned for my next blog, where I might talk about one more probability distribution.