Robust measures of tail weight

The kurtosis coefficient is often regarded as a measure of the tail heaviness of a distribution relative to that of the normal distribution. However, it also measures the peakedness of a distribution, hence there is no agreement on what kurtosis really estimates. Another disadvantage of the kurtosis is that its interpretation and consequently its use is restricted to symmetric distributions. Moreover, the kurtosis coefficient is very sensitive to outliers in the data. To overcome these problems, several measures of left and right tail weight for univariate continuous distributions are proposed. They can be applied to symmetric as well as asymmetric distributions that do not need to have finite moments. Their interpretation is clear and they are robust against outlying values. The breakdown value and the influence functions of these measures and the resulting asymptotic variances are discussed and used to construct goodness-of-fit tests. Simulated as well as real data are employed for further comparison of the proposed measures.