Abstract
The (symmetric) trimmed mean estimator truncates the same number of samples at both of sides of the probability distribution. For asymmetric distributions the problem is to decide where to truncate the distribution on the left and right side. A generalized asymmetric Gaussian distribution that covers a wide range of length of tails and asymmetry is proposed and employed to approximate the distribution of this discrete data. Using this distribution, truncation points of the discrete distribution on both sides have been obtained. Starting with the trimmed mean estimator that can be used for symmetrically distributed data, an adaptive generalized trimmed mean (AGTM) estimator is developed and employed to estimate the third-order cumulants. Using these truncation parameters the AGTM of the discrete data series are computed and it is seen that the AGTM performs better in estimating third-order comulants than the mean estimator.
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