# Poisson Distribution

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Related to Poisson random variable: Exponential random variable, Hypergeometric random variable

## Poisson Distribution

In statistics, a distribution representing the probability of a random event that occurs at regular intervals on average. Each event occurs independently of every other one.
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Throughout this section, without any other specification, the number M of planes is assumed to be a Poisson random variable, so that Eq.
Therefore, when the zero-truncated Poisson random variable X has the same mean as that of its mixture Y, then there is no simple stochastic ordering between X and Y.
Since the number of vessels scrapped each period are discrete, we assume that the number of scrapped vessels for each category (we assign for categories of vessels, based on tonnage (capacity)) follows a Poisson process and consequently the sum across all categories is the sum of Poisson processes following a Poisson process, too (The distribution of the Poisson random variable and the associated properties are presented in Appendix A).
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