MCE {CircOutlier}

Detection of Outliers in Circular-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

parameter k.

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

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.

Value

Number, that is mean circular error.

Author(s)

Azade Ghazanfarihesari, Majid Sarmad

References

A. H. Abuzaid, A. G. Hussin & I. B. Mohamed (2013) Detection 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)