In the present work, a weighted maximum likelihood method (WMLM) is proposed to obtain robust estimates of experimental data containing outliers. The method allows asymptotically effective robust unbiased estimates to be obtained in the presence of not only external, but also internal asymmetric and symmetric outliers. Algorithms for obtaining robust WMLM estimates are considered at the parametric level of aprioristic uncertainty. It is demonstrated that these estimates converge to the maximum likelihood estimates of a heterogeneous data sample for each distribution within the Tukey supermodel.
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