Suchergebnisse

It is a matter of common observation that investors value substantial gains but are averse to heavy losses. Obvious as it may sound, this translates into an interesting preference for right‐skewed return distributions, whose right tails are heavier than their left tails. Skewness is thus not only a way to describe the shape of a distribution, but also a tool for risk measurement. We review the statistical literature on skewness and provide a comprehensive framework for its assessment. Then, we present a new measure of skewness, based on the decomposition of variance in its upward and downward components. We argue that this measure fills a gap in the literature and show in a simulation study that it strikes a good balance between robustness and sensitivity.

Groeneveld (1986) in discussing the skewness for the Weibull family has pointed out the shortcomings of the classical measures of asymmetry—the standardized third moment and the Pearson measure of skewness. He has shown that a modified form of the Pearson measure b3= (μ‐m)/E|X‐m| portrays the skewness of Weibull family quite well. We give another competitive measure of skewness T that is easy to interpret and is based on conditional expectations. The proposed measure satisfies the desirable properties of a skewness measure.

Abstract. The skewness of the Weibull family of distributions is discussed for all values of the shape parameter. This class includes unimodal probability densities for which the coefficient of skewness μ3/o3 is positive, but the order of the mean, median and mode is μ < m < M. For values of the shape parameter used in practice the distributions are skewed to the right by a well accepted definition of skewness.