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Exponential Distribution — Intuition, Derivation, and Applications

When to Use an Exponential Distribution

Aerin Kim
Towards Data Science
8 min readAug 6, 2019

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Before diving into the formulas, it’s crucial to understand the “why” behind the exponential distribution. With a solid grasp of the underlying principles, you’ll be more likely to apply this knowledge effectively in your own work.

1. Why did we have to invent Exponential Distribution?

Exponential distribution is often used to predict the waiting time until the next event occurs, such as a success, failure, or arrival.

For example, Exponential Distribution can be used to predict:

  • The amount of time it takes a customer to make a purchase in your store (success)
  • The amount of time until hardware on AWS EC2 fails (failure)
  • The amount of time you need to wait for the bus to arrive

Then, my next questions would be: Why is λ * e^(−λt) the PDF of the time until the next event happens? What does X ~ Exp(0.25) mean?

Does the parameter 0.25 represent 0.25 minutes, hours, or days, or is it 0.25 events?

From this point on, I’m going to assume that you know the Poisson distribution well. If you don’t, this article will explain it to you.

X ~ Exp(λ) 👉 Is the exponential parameter λ the same as λ in Poisson?

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Towards Data Science
Towards Data Science

Published in Towards Data Science

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Aerin Kim
Aerin Kim

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