Development of an adaptive generalised trimmed mean estimator to compute third-order cumulants

Abstract

An adaptive generalised trimmed mean (AGTM) estimator for both symmetric and asymmetric unimodal distributions is developed in this paper. For asymmetric probability density functions (pdf 's) the problem is to decide where to truncate the pdf on the left and the right side. To solve this problem, an extended generalised Gaussian distribution that covers a wide range of length of tails and asymmetry by varying two parameters is employed to approximate the distribution of the available data. From this approximated distribution, truncation points on both sides of the measured distributions are obtained. The AGTMs of the discrete time series are employed in the estimation of the third-order cumulants of many zero-mean symmetric as well as asymmetric data, including the output from many autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) systems with simulated input signals from various pdf's.