R 中围绕 (x,y) 点的正态分布的 3D 图 [英] 3D Plot of normal distribution in R around a (x,y) point

问题描述

我想在 (x,y,z) 坐标系上绘制正态分布的单变量正态密度函数.我使用的代码是:

I want to plot a univariate normal density function of the normal distribution onto a (x,y,z) coordinate system. The code I am using is:

library(rgl)
open3d()

x <- seq(0, 10, length=100)
y <- seq(0, 10, length=100)


z = outer(x,y, function(x,y) dnorm(x,2.5,1)*dnorm(y,2.5,1))

persp3d(x, y, z,col = rainbow(100))

我遇到的问题是，我希望正态分布不仅仅围绕其均值，而且要在一条直线或一个圆上.在后一种情况下，我希望输出类似于火山.我想我必须首先在循环中创建一些概率.我怎样才能做到这一点?或者我也应该使用一些表面命令来绘制输出?我很确定这与二元正态无关.

The problem I an encountering is that I want the normal distribution not to be around its mean only but also to be on a straight line or a circle. In latter case, I would expect the output to be similar to a volcano. I guess I must first create some probabilities within a loop. How can I do this? Or should I also use some surface command to plot the output? I am pretty sure this has nothing to do with a bivariate normal though.

最好的富士

推荐答案

第一部分很简单:只是不要让你的 z 依赖于 y 例如:

The first part is easy: just don't let your z depend on y for instance:

z = outer(x,y, function(x,y) dnorm(x,2.5,1))
persp3d(x, y, z,col = rainbow(100))

对于第二部分，您可以想象正态分布的均值位于 x^2+y^2=1 圆上.您将拥有径向方向的无限正态分布.试试这个:

For the second part, you can imagine that the means of the normal distribution lie on the x^2+y^2=1 circle. You will have infinite normal distributions with radial directions. Try this:

#define the volcano function
volcano<-function(x,y,sigma=1/2) {
  alpha<-atan(y/x)+pi*(x<0)
  d<-sqrt((cos(alpha)-x)^2 + (sin(alpha)-y)^2)
  dnorm(d,0,sigma)
}
x<-seq(-2,2,length.out=100)
y<-seq(-2,2,length.out=100)
z<-outer(x,y,volcano)
persp3d(x, y, z,col = rainbow(100))

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