Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation...

Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation...

Using the Gaussian distribution as statistical model for data sets is widely spread, especially in practice. However, departure from normality seems to be more the rule than the exception. The H-distributions, introduced by Tukey (1960, 1977), are generated by a single transformation...

There are several possibilities to introduce skewness into a symmetric distribution. One ofthese procedures applies two di®erent parameters of scale { with possibly di®erent weights {to the positive and the negative part of a symmetric density. Within this work we show thatthis technique...

Two major generalizations of the hyperbolic secant distributionhave been proposed in the statistical literature which both introduce an additionalparameter that governs the kurtosis of the generalized distribution. Thegeneralized hyperbolic secant (GHS) distribution was introduced by Harknessand...

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...

The H−family of distributions or H−distributions, introduced byTukey (1960, 1977), are generated by a single transformation of the standard normal distribution and allow for leptokurtosis represented by the parameter h. Alternatively, Haynes, MacGillivray and Mengersen (1997) generated...

It is well known that the arithmetic mean of two possibly differentcopulas forms a copula, again. More general, we focus on theweighted power mean (WPM) of two arbitrary copulas which is notnecessary a copula again, as different counterexamples reveal. However,various conditions regarding the...