如何计算圆形数据的标准偏差 [英] How to calculate standard deviation of circular data
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问题描述
我已遵循此处提出的建议来计算循环数据的平均值:
I've followed the advice laid out here for calculating the average of circular data:
https://en.wikipedia.org/wiki/Mean_of_circular_quantities
但是我也想计算标准差.
But I'd also like to calculate standard deviation as well.
#A vector of directional data (separated by 20 degrees each)
Dir2<-c(350,20,40)
#Degrees to Radians
D2R<-0.0174532925
#Radians to Degrees
Rad2<-Dir2 * D2R
Sin2<-sin(Rad2)
SinAvg<-mean(Sin2)
Cos2<-cos(Rad2)
CosAvg<-mean(Cos2)
RADAVG<-atan2(SinAvg, CosAvg)
DirAvg<-RADAVG * R2D
以上是我的平均值,但我不知道如何计算SD
The above gives me the average, but I don't know how to calculate the SD
我试图只取正弦和余弦的标准偏差的平均值,但是得到的答案却不尽相同.
I tried to just take the mean of the standard deviation for both the sine and cos, but I get varying answers.
SinSD<-sd(Sin2)
CosSD<-sd(Cos2)
mean(CosSD, SinSD)
推荐答案
您可以为此使用circular
包:
x <- circular(Rad2)
mean(x)
# Circular Data:
# Type = angles
# Units = radians
# Template = none
# Modulo = asis
# Zero = 0
# Rotation = counter
# [1] 0.2928188 # The same as yours
sd(x)
# [1] 0.3615802
手动
sqrt(-2 * log(sqrt(sum(Sin2)^2 + sum(Cos2)^2) / length(Rad2)))
# [1] 0.3615802
可以从sd.circular
的源代码中看到.
which can be seen from the source code of sd.circular
.
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