CircOutlier (version 3.1.4)

MCE: Detecting of Outliers in Circular Regression

Description

Mean circular error

Usage

MCE(y,Y,n)

Arguments

y

observed values of the response variable are calculated based on model $y_i=\alpha+\beta x_i+\epsilon_i$(mod 2$\pi$) (i=1,2,...,n). here n is sample size. random error having a VonMises distribution with circular mean 0 and concentration

Y

the estimeted value of y under model $y_i=\alpha+\beta x_i+\epsilon_i$(mod 2$\pi$) (i=1,2,...,n).

n

the sample size

Value

• Number, that is mean circular error.

Details

This function may be considered as a type of arithmetic mean which is not robust to the existence of outlier.thus it can be used to detect the possible outliers in the circular regression.

References

A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detecting of outliers in simple circular regression models using the mean circular error statistics.

See Also

circular, CircStats

Examples

#Generate a data set dependent of circular variables.
library(CircStats)
n <- 50
x <- rvm(n = 50, 0, 2)
y <- rvm(n = 50, pi/4, 5)
# Fit a circular-circular regression model.
circ.lm <- circ.reg(x, y, order = 1)
Y <- circ.lm$fitted
MCE(y, Y, n)