有很多种方法都可以推导出正态分布公式,这里将介绍一种既优雅又直观的推导方式,由天文学家赫歇尔(John Herschel) [^5] 在 1850 年给出的。3Blue1Brown的视频Why π is in the normal distribution (beyond integral tricks)中详细介绍了这种方式。不过...
学过中学数学都知道,在正态分布(Normal Distribution)[2]中,68.27%的数据位于平均值的一个标准差内,95.45%位于两个标准差内,99.73%位于三个标准差内,这也是著名的 68-95-99.7 Rule[3],如下图 1 所示: 图1. 68-95-99.7 Rule 什么是正态分布? 数据可以用不同的方式“分布”,比如数据可以向左散布的多一...
[8]: 高斯积分 Gaussian integralhttps://en.wikipedia.org/wiki/Gaussian_integral [9]: 中心极限定理...
normal distribution normal dwarf Normal equation Normal equations normal fault Normal group normal hill normal impact effect normal intelligence reports normal lighting normal matrix normal mode normal operations Normal place normal school Normal spectrum ...
Normal Distribution Definition The Normal Distribution is defined by theprobability density functionfor a continuous random variable in a system. Let us say, f(x) is the probability density function and X is the random variable. Hence, it defines a function which is integrated between the range ...
一个叫黎曼的德国数学家(Bernhard Riemann, 1826-1866),他想了个办法:将这不规则图形切成一条条的小长条儿,然后将这个长条近似的看成一个矩形,再分别测量出这些小矩形的长度,再计算出它们的面积,把所有矩型面积加起来就是这块不规则地的面积。这就是著名的“黎曼和”。小长条宽度趋于0时,即为面积微分,各个...
Integral of Normal DistributionJonathan M. Lees
On the surface of cylindrical bounday,with the help of the series expansion of elliptic integration,the integration for the lateral surface of a cylinder has been expressed in analytical form about the integral equation of electric log. 在柱状边界条件下 ,借助椭圆积分的级数展开将电测井积分方程中...
//idan-alter.github.io/2023/02/..And if you d like to see many other variations on approaching this integral,take a look at this expository paper from Keith Conrad:https://kconrad.math.uconn.edu/blurbs...Timestamps:0:00-The statistician s friend 3:44-The classic proof 12:47-The ...
This distribution function can be converted to the following cumulative mass basis distribution: (1.9)D=1002πlnσ∫−∞lnδexp−lnδ−lnδ5022δ2dlnδ where δ50 is the median mass diameter and lnδ is the standard deviation of log diameters from their mean magnitude. The integral conta...