M-estimator with asymmetric influence function for estimating the Burr type III parameters with outliers

The Burr type III distribution allows for a wider region for the skewness and kurtosis plane, which covers several distributions including the log-logistic, and the Weibull and Burr type XII distributions. However, outliers may occur in the data set. The robust regression method such as an M-estimator with symmetric influence function has been successfully used to diminish the effect of outliers on statistical inference. However, when the data distribution is asymmetric, these methods yield biased estimators. We present an M-estimator with asymmetric influence function (AM-estimator) based on the quantile function of the Burr type III distribution to estimate the parameters for complete data with outliers. The simulation results show that the M-estimator with asymmetric influence function generally outperforms the maximum likelihood and traditional M-estimator methods in terms of the bias and root mean square errors. One real example is used to demonstrate the performance of our proposed method.