Estimation of parameters in the presence of outliers for a burr XII distribution

Abstract

This paper deals with an unweighted least squares (LS) estimation of the parameters of a two-parameter Burr XII distribution and compares the results with the maximum likelihood (ML) and maximum product of spacings (MPS) methods. The performance of these estimators is examined with and without outliers through simulation studies. Also, we obtain approximate confidence intervals for the parameters c and k. We propose that the LS method when data, yi are generated by using log log [n/(n — i -f 0.5)) for small n be preferred over the ML and MPS methods, while for large samples the ML method has a slight edge over the LS method in terms of root-mean squared error (RMSE). However, the amount of computer time required by the ML method in solving the simultaneous equations negates this advantage.

Keywords:

• Maximum likelihood estimator
• least squares estimator
• maximum product of spacings
• root-mean squared error
• mean shift model
• outliers