Introduction
A Poisson distribution is a distribution that shows the likely number of times that an event will occur within a pre-determined period of time. It is used for independent events which occur at a constant rate within a given interval of time.
Poisson distribution is
- Discrete
- Used for count-based data
The Poisson distribution, named after the French mathematician Denis Simon Poisson, is a discrete distribution function describing the probability that an event will occur a certain number of times in a fixed time (or space) interval. For example, the number of mails in your mailbox arriving equals the number of customers arriving at a shop.
Mathematical Definition
A Poisson distribution is a distribution that shows the likely number of events occurring in a specific period of time. It is used for independent events which occur at a constant rate within a given interval of time. The Poisson distribution is a discrete function, meaning that the event can only be measured as occurring or not as occurring, meaning the variable can only be measured in whole numbers.
Let’s consider an example, Hema is recording birds in a national park, using a microphone placed in a tree. She is counting the number of times a bird is recorded singing and wants to model the number of birds singing in a minute. For this task, she’ll assume the independence of the detected birds.
We use the seaborn python library which has in-built functions to create such probability distribution graphs. Also, the scipy package helps in creating the binomial distribution.
The Poisson distribution is denoted as
Poi is expressed as follows:
for
k=0,1,2,…
K = events given the parameter
λ = corresponds to the expected number of occurrences in that time slot.
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