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What is Poisson Distribution?

Poisson random variables are used to measure counts of events.

What is Poisson Distribution?

Poisson random variables are used to measure counts of events. Poisson random variables are always non-negative and integer-valued. The Poisson Distribution has a single parameter called the hazard rate and is expressed as λ, which signifies the average number of events per interval. Therefore, the mean and variance of Y ~ Poisson(λ) are:

E[Y] = V[Y] = λ

PMF of Poisson:

$ f(Y)y= \frac{\lambda ^{y}exp(-\lambda)}{y!} $

CDF of Poisson:

Meanwhile, the CDF of a Poisson is defined as the sum of the PMF for values less than the input.

$ F(Y)_{y}= exp(-\lambda )\sum_{i=0}^{y}\frac{\lambda ^{i}}{i!} $

Why is Poisson Distribution important?

A Poisson distribution is a tool that helps to predict the probability of certain events happening when you know how often the event has occurred. It gives us the likelihood of a given number of events happening in a fixed time interval. One application of a Poisson is to model the number of loan defaults that occur each month.

Owais Siddiqui
1 min read
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