Why do we sometimes need to predict rare events?
Exponential distribution
Why do we sometimes need to predict rare events?
Imagine you're planning a big event and want to know how likely it is that something rare, like a power outage, will disrupt your plans.
Think of rare events as happening at random times, like raindrops falling on a sidewalk. The Poisson distribution helps us guess how many raindrops (or disruptions) we'll get in a given time.
Example
If power outages happen on average once every 100 days, the Poisson distribution helps us predict the chance of experiencing 0, 1, 2, or more outages in any 100-day period.
Remember this
The Poisson distribution is the maximum entropy distribution for a fixed mean because it maximizes uncertainty, making it the most unbiased prediction of rare events given an average rate.
Text adapted from Wikipedia, licensed under CC BY-SA 4.0.
Related concepts
log-probabilities are used instead of probabilities: avoids numerical underflow
Why can't we just add up tiny chances over time?
Rényi entropy
How do we measure the unpredictability of an event?
Markov's inequality
Ever wondered how math can predict unlikely events?
Likelihood function
Why can't we just guess probabilities correctly all the time?
Entropy H = -Σ p(x) log₂ p(x) measures average surprise in bits
How do we measure uncertainty in everyday decisions?
the Dirichlet distribution does: distribution over probability simplices
How do we predict the likelihood of various outcomes in uncertain situations?
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