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这是一种可以用来描述和分析随机地分布在单位空间里的稀疏微粒数(例如一升饮水中的大肠菌数,计数器小方格中的血球数)或随机地发生在单位时间里的少见事件数(如某市一天中的车祸数,某厂一周中的工伤事故数)的分布。是法国人S.D.Poisson(1781～1840)作为二项分布的一种极限导出的。有着广泛的用途,而且也是统计学的基本理论的重要组成部份。1 基本概念如果一种服从二项分布的随机事件(或现象)的发生(阳性)率很小(接近0),而样本的含量n 很大(趋向∞),同时它的平均数np=μ为一客观常数,则其方差σ~2=npq=np(因q 接近1)=μ,即方差与均数相等。这种分布称为泊松分布,它的分布列如下
This is a method that can be used to describe and analyze the number of sparse particles randomly distributed in the unit space (such as the number of coliform bacteria in a liter of drinking water, the number of blood cells in a counter square) or randomly occurring in unit time. The number of rare incidents (such as the number of accidents in a day in a city, the number of workplace accidents in a factory). It was the French S.D. Poisson (1781~1840) that was derived as a limit of the binomial distribution. Has a wide range of uses, but also an important part of the basic theory of statistics. 1 Basic Concepts If the incidence (positive) of a random event (or phenomenon) obeying the binomial distribution is small (close to 0), and the content n of the sample is large (towards ∞), and its average number np = μ For an objective constant, the variance σ~2=npq=np (because q is close to 1) = μ, that is, the variance is equal to the mean. This distribution is called the Poisson distribution and its distribution is as follows