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

The Burr type III distribution allows a wider region for the skewness and kurtosis plane, which covers several distributions including: the log-logistic, the Weibull and the Burr type XII distributions. However, outliers may occur in the data set. The robust regression method has been successfully used to diminish the effect of outliers on statistical inference. This paper presents an M-estimator based on the quantile function to estimate the Burr type III parameters for complete data with outliers. We showed that all regularity conditions are satisfied for the normal approximation of the Burr type III distribution using the M-estimator. Thus, the confidence intervals for all parameters can be obtained. The simulation results showed that the M-estimator generally outperforms the maximum likelihood and least squares methods regarding bias, root mean square errors and a number of quantile values. One real example and one simulated data example are used to demonstrate the performance of our proposed method.