Kurtosis transformation and kurtosis ordering

Leptokurtic distributions can be generated by applying certainnon-linear transformations to a standard normal random variable. Withinthis work we derive general conditions for these transformations which guaranteethat the generated distributions are ordered with respect to the partialordering of van Zwet for symmetric distributions and the partial orderingof MacGillivray for arbitrary distributions. In addition, we propose a generalpower transformation which nests the H-, J- and K-transformationswhich have already been proposed in the literature. Within this class of powertransformations the above mentioned condition can be easily verified and thepower can be interpreted as parameter of leptokurtosis.