Poisson Distribution is a probability distribution that is used to model the number of occurrences of a specific event within a fixed time or space, given that the occurrences are independent and the average rate of occurrence is constant.
Poisson Distribution is different from other probability distributions in that it is used to model discrete events that occur at a constant rate, rather than continuous events or events that occur randomly. It is also unique in that the mean and variance of the distribution are equal.
The key characteristics of Poisson Distribution include its probability mass function, which calculates the probability of a specific number of occurrences, and its mean and variance, which are both equal to the parameter lambda (λ).
Poisson Distribution is commonly used in real-world applications to model events such as number of customers in a queue, number of emails received per day, or number of accidents on a highway. It is also used in fields such as finance, biology, and telecommunications to model various discrete events.
Poisson Distribution has several limitations, including the assumption of a constant rate of occurrence, which may not always be true in real-world situations. It also does not account for events that are dependent on each other or for rare events with low probabilities. Additionally, it is not suitable for modeling continuous or continuous-time events.