MOMENTS ABOUT SMALLEST SAMPLE VALUE

Abstract
A new type of moments has been achieved by substituting in the central moments the smallest value of the sample for its mean. The new moments have the same advantage as the central moments of being independent of the location parameter but for certain value of the shape parameter they have less variance and thus are preferable for estimating purposes. The asymptotic properties of four estimators, three of them composed of the new moments and one of them of central moments have been examined. It could be concluded that for the shape parameter alpha = or is 0.5 the estimator, which was composed of the first and second order moments of the new type, was by far the most efficient one. Small-sample properties of the new-moments estimators have been appraised by use of extensive Monte-Carlo studies and it could be stated that the same conclusion applies also to small and moderate sample sizes.

This publication has 0 references indexed in Scilit: