Abstract

Non-negative data arises in numerous fields. Self-inverse log-symmetric distributions provide an opportunity to construct estimators of distribution parameters that are more efficient than the corresponding well-known moment estimators, leading, in general, to more accurate modeling of non-negative real data. This paper presents a review of a number of self-inversion-based estimators that have been developed during the past ten to twelve years, and presents a new self-inversion-based estimator of the rth moment about the mean, thus adding to the list. A simulation study is presented to demonstrate that the newly developed estimator is more efficient than the corresponding estimator obtained by the ordinary method of moments. The advantageousness of the newly proposed estimator for purposes of model-fitting as compared with the ordinary moment estimator is demonstrated through application to two real data-sets.