1. The concept of Poisson distribution (poisson distribution)

The Poisson distribution is also a discrete distribution used to describe the probability distribution of the number of occurrences of rare events .

The Poisson distribution can also be used to study the distribution of the number of occurrences of a rare event per unit time (or unit space, volume):

Analyze the distribution of bacterial counts per unit area or volume,
The distribution of the number of certain insects or wild animals in a unit space,
the distribution of dust within the observation volume,
The distribution of the number of particles emitted by radioactive substances per unit time, etc.

The Poisson distribution is generally denoted as $\pi \left ( \lambda \right )$ or $P\left ( \lambda \right )$ .

2. The Poisson distribution is a limiting case of the binomial distribution

The Poisson distribution can be regarded as a binomial distribution when the probability of occurrence $\pi$ is small and the number of observations is large .

In addition to meeting the three basic conditions of the binomial distribution , the Poisson distribution also requires $\pi$ or 1- $\pi$ close to 0 and 1 . Some situations $\pi$ and n are difficult to determine, and can only be expressed by the number X of a rare event in the observation unit (time, space, volume, area), such as the number of E. coli per milliliter of water, the number of dust in each observation unit Counting, the number of radioactive particles per unit time, etc., as long as bacteria, dust, and radioactive pulses meet the above conditions within the observation time, they can be approximated as Poisson distribution.