(40 minutes to learn)
The exponential distribution is a continuous distribution whose PDF decays exponentially. It is most commonly used to model the waiting time until an event occurs, where that event is equally likely to happen at any point in time.
This concept has the prerequisites:
Core resources (read/watch one of the following)
→ A First Course in Probability
An introductory probability textbook.
Location: Section 5.5, "Exponential random variables," pages 230-236
→ Probability and Statistics
An introductory textbook on probability theory and statistics.
Location: Section 5.9, "The gamma distribution," starting with "The exponential distribution," pages 298-301
→ Mathematical Statistics and Data Analysis
An undergraduate statistics textbook.
Location: Section 2.2.1, "The exponential density," pages 50-52
- The gamma distribution is a generalization of the exponential distribution.
- The geometric distribution is a geometric analogue of the exponential distribution.
- The exponential distribution is the only memoryless continuous distribution.
- Equivalently, it is the only continuous distribution with constant failure rate .
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