在 R 中绘制圆形随机变量的 PDF（极坐标图）

Question

I am trying to find a sensible way of visualising probability density functions of circular random variables in R. The most appropriate way of doing so is on a polar plot. However, I am not sure how to code this in R. Can someone illustrate how this can be done, using the wrapped exponential distribution as an example? I'd really appreciate it.

Answer 1

The circular package seems focused on vonMises distribution. You can roll your own wrapped exponential probability distribution:

wrapped.exp <- function(theta, lambda){ 
                          lambda*exp(-lambda*theta)/(1-exp(-2*pi*lambda) )}

And use plotrix package's radial.plot :

theta <- seq(0, 2*pi, len=100)
rval <- wrapped.exp(theta, .2)
# radial.plot's default radial limits are just the range so not really good for distributions.
radial.plot(rval,theta, radial.lim=c(0, 0.4))

Plotting code:

> png()
> rval <- wrapped.exp(theta, .2)
> radial.plot(rval,theta, radial.lim=c(0, 0.4))
> dev.off()

I would note that the "wrapped exponential" formula is not actually a true mathematical function on the closed interval [0, 2*pi] since this function would have two values at 0 = 2 pi, so it probably should have code to make any theta + or > 2 pi to be NA or something "mod 2 pi". Further note: That formula is really just a truncated exponential at 2 pi. Since it is a truncated density it seems that it should not have a 0 value at 2*pi. Appears that radial plot uses the range of the radial vector rather than going from 0 to maximum. Seems that it should default instead to c(0, range(lambda)[2]). When I get time I will correct this answer.

Answer 2

The ezpolar function from pkg:pracma gives a more typical polar plot than plotrix::radial.plot , however it is like the base graphics function curve in that it takes a functional argument.

if(!require(pracma) ){ 
         install.packages("pracma", dependencies=TRUE); library(pracma) }
?ezpolar
wrapped.exp <- function(theta, lambda){ 
                      lambda*exp(-lambda*theta)/(1-exp(-2*pi*lambda) )}
theta <- seq(0, 2*pi, len=100)

# since it requires a functional argument with only one variable,
# I'm defining a separate helper function with predefined lambda

  png() ;  wrap.2 <- function(x) wrapped.exp(x,.2)
           ezpolar(wrap.2); dev.off()