Page 113 - Special Topic Session (STS) - Volume 1

STS410 Abdul Ghapor H. et al.

A technique for outliers detection in linear
functional relationship model for circular
variables
1
Abdul Ghapor Hussin , Nurkhairany Amyra Mokhtar , Yong Zulina Zubairi ,
2
1
Mohd Iqbal Shamsudheen 3
1 National Defence University of Malaysia
2 University of Malaya
3 University College London

Abstract
The occurrence of outlier may be due to error, or part of the phenomena under
study. This paper discusses on outlier detection methods are discussed using
difference mean circular error cosine statistic for circular variables. Here, we
focus on a model with linear functional relationship model in which the
variables are considered with equal concentration of their error terms. The cut-
off equation for outlier detection is obtained by using row deletion approach
and it is then tested to detect the outlier in a simulation study. The power of
performance of this method increases as the concentration parameters of the
errors and the level of contamination for the outlier increase. The applicability
of this method is illustrated by using real wind direction data.

Keywords
Outlier detection; Circular variables; Row deletion; Power of performance;
Simulation study

1. Introduction
Directional data arises quite frequently in many natural and physical
sciences. The directions may be in two-dimensional or in three-dimensional.
Observations on two-dimensional directions can be referred as circular data
meanwhile the observations on three-dimensional directions can be referred
as spherical data (Jammalamadaka and Sengupta (2001)).
An example of circular data is the data of wind directions. The distribution
of the directions may arise either as a conditional distribution for a given
speed, or as a marginal distribution of the wind speed and direction. The Von
Mises distribution is said to be the most useful distribution on the circle
(Mardia and Jupp (2000)). Fisher (1987) noted that the Von Mises distribution
is a symmetric unimodal distribution and characterised by a mean direction
 and concentration parameter . The probability density function of the

distribution is

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