Several authors have concluded that the standardized fourth central moment of a symmetric distribution is not a good measure of the shape of a distribution. Here we consider the properties of a class of parameters of a distribution based on its percentiles, as alternative measures of kurtosis. It is shown that this scale and location invariant measure maintains the symmetric ordering of van Zwet. Influence functions are used to show how this measure reflects the kurtosis of a distribution. Results of a simulation study indicate that the power of the Shapiro-Wilk test, for a large number of symmetric distributions alternative to the normal distribution, is almost linear as a function of appropriate functionals in this class. This suggests the use of this functional as a kurtosis measure.