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概率密度(质量)函数:
高斯分布:
高斯分布是连续性的分布。其中u是均值,^2是方差。
二项分布:
其中,k是一系列的离散值,因为二项分布是一个离散分布,代表某时间成功(发生)的概率为p,
则在n次的抽样过程中,成功(或发生)了k次,不成功(不发生)的次数为n-k次,此时按照上式计算出严格叫概率质量函数(因为其离散),
其均值为n*p,方差为n*p*(1-p)。
泊松分布:
同样的,泊松分布也是一个离散的分布,其中
为某事件在单位时间内发生的次数,k为变量。泊松分布的物理意义为在一段时间内,时间X发生了k次的概率质量,泊松分布的均值和方差全部为
。
三种分布之间的转换关系具体如下:
二项分布泊松分布:当样本数n趋向于无穷,概率p趋向于0,n*p趋向于一个常数时,二项分布可以近似看作一个泊松分布。
二项分布高斯分布:当样本数n趋向于无穷的时候,二项分布可以近似看作一个高斯分布。
泊松分布
高斯分布:当泊松分布的均值趋向于无穷时,泊松分布既可以近似为一个高斯分布,即泊松分布的均值越大,与高斯分布的区别就越小。(以上趋向于无穷不是指取值为无穷,是取一个值相对较大的数即可)。
个人理解, 若有错误,请批评指正!!!