A few remarks on the estimation of some variability measures
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This paper intends to highlight a few considerations on the choice of a variability measure and its estimate, focusing on the standard deviation, the mean deviation and the mean difference. We have considered the non-parametric case, the normal and the Pareto distribution. All the examined characteristics point out that the mean difference can be re-evaluated. The sample mean difference presents exact results in terms of expected value and variance, moreover this variance exists finite
even if, in the parent population, the moments of order greater than two are infinite; instead the approximate variance of the sample standard deviation is finite only if, in the parent population, the fourth moment is finite. This aspect should be taken into account when the observed data are well described by a heavy tail distribution
model. In the normal distribution the estimator of the standard deviation based on the sample mean difference has the variance very close to that of the estimator
based on the sufficient statistics.
Keywords: standard deviation, mean deviation, mean difference, unbiased estimator, mean square error. Author biographyMarcella Polisicchio, Dipartimento di Metodi Quantitativi per le Scienze Economiche e Aziendali – Università degli Studi di Milano-Bicocca – Piazza dell’Ateneo Nuovo, 1, 20126 MILANO (e-mail: marcella.polisicchio@unimib.it). |
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