Il giorno Martedì 15 Novembre 2011 alle ore 11.15 presso l'Aula Consiglio, Ala 2C secondo piano (ex Dipartimento di Statistica) si terrà un seminario tenuto dal J.F. Rosco Nieves (Università dell'Estremadura) dal titolo
SKEWNESS - INVARIANT MEASURES
central moment is a characteristic used to describe the shape of a probability distribution. However, since its introduction more than a century ago, numerous interpretations of it have been suggested within the literature. A historical review of these interpretations is made and the measurement of kurtosis in the presence of asymmetry is considered. Blest’s kurtosis measure adjusted for skewness is studied and an alternative coefficient is proposed, both measures also being based on moments. Since the existence of moments of a distribution cannot always be assured, a quantile-based approach is considered. Two forms of kurtosis measures based on quantiles are identified which are invariant to the presence of skewness for certain families of distributions obtained via the transformation of a base symmetric random variable. A very general condition is established which can be used to determine when the two types of kurtosis measures will be skewness invariant, and two wide families of distributions are identified for which the measures are skewness invariant. These two family of distributions are the well-known Johnson’s unbounded family and the more recently proposed sinh-arcsinh family. Also we identify a family of distributions not arising via transformation for which the measures are skewness invariant, namely the Tukey lambda family.
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