SB-robust estimator for the concentration parameter of circular normal distribution

Abstract

In this paper we discuss robust estimation of the concentration parameter (κ) of the circular normal (CN) distribution. It is known that the MLE of the concentration parameter is not B-robust at the family of all circular normal distributions with fixed mean direction (μ) and varying κ > 0. In this paper we propose a new estimator for κ and show that it is B-robust and SB-robust at the family {CN (μ, κ) : m ≤ κ ≤ M} where m and M are two arbitrary constants.

SB-Robust Estimators of the Parameters of the Wrapped Normal Distribution

“…Definition 5.1 (Laha and Mahesh, 2012). Let be the trimming proportion such that 0 ≤ < 0 5 and are such that:…”

“…Now, if an estimator T is SB-robust at the family of distributions for one of these dispersion measures then it must be SB-robust at the family of distributions for the other dispersion measure. Laha and Mahesh (2012) discussed the SB-robustness of some estimators of the concentration parameter of the circular normal distribution.…”