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...

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

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...

Tukey (1960) derived via the technique of transformation of variables starting from the normal distribution a family of skewed and leptokurtic distributions. Skewness and leptokurtosis are determined by two parameters g and h. Therefore, the family was called family gh-distributions. We modify...

Sample size analysis is a key part of the planning phase of any research. So far, however, limited literature focusses on sample size analysis methods for two-sample linear rank tests, although these methods have optimal properties at different distributions. This paper provides a new sample...

Skewness is a well-established statistical concept for continuous and to a lesser extent for discrete quantitative statistical variables. However, for ordered categorical variables almost no literature concerning skewness exists, although this type of variables is common for behavioral,...

Jaynes (1957a,b) formulates the maximum entropy (ME) principle as the search for a distribution maximizing a given entropy under some given constraints. Kapur (1984) and Kesavan & Kapur (1989) introduce the generalized maximum entropy principle as the derivation of an entropy for which a given...