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<>概率论中 PDF,PMF,CDF的含义
在概率论中,我们经常能碰到这样几个概念PDF,PMF,CDF,这里就简单介绍一下
PDF:概率密度函数(probability density function),
在数学中,连续型随机变量的概率密度函数(在不至于混淆时可以简称为密度函数)是一个描述这个随机变量的输出值,在某个确定的取值点附近的可能性的函数。
概率密度函数都是针对连续性随机变量的,对于连续性随机变量,都是针对某一段区间的取值,在一个点的取值都是几乎为0的,所以我们研究连续性随机变量时,都是取变量在一段区间的取值,然后可以通过概率密度函数进行计算。
而PDF他其实是CDF的导数。
PMF : 概率质量函数(probability mass function), 在概率论中,概率质量函数是离散随机变量在各特定取值上的概率。
PDF是针对连续型随机变量的,那么PMF则是针对离散型随机变量的,是变量在特定取值上的概率。
CDF : 累积分布函数 (cumulative distribution
function),又叫分布函数,是概率密度函数的积分,能完整描述一个实随机变量X的概率分布。
累计分布函数则比较是说,我们取定一个值,计算变量小于这个值的概率。