Velleman & Wilkinson (1993) give a lot of examples to show that the hierarchy of scalers introduced by Stevens is misleading. We will show that these examples gain are misleading if we accept that most real data sets stem come derived measurement. For derived measurement the absolute scale is...

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two...

We will identify sufficient and partly necessary conditions for a family of copulas to be closed under the construction of generalized linear mean values. These families of copulas generalize results well-known from the literature for the Farlie-Gumbel-Morgenstern (FGM), the Ali-Mikhai-Haq (AMH)...

We will identify sufficient and partly necessary conditions for a family of copulas to be closed under the construction of generalized linear mean values. These families of copulas generalize results well-known from the literature for the Farlie-Gumbel-Morgenstern (FGM), the Ali-Mikhai-Haq (AMH)...

There are several procedures to construct a skewed distribution. One of these procedures splits the value of a parameter of scale for the two halfs of a symmetric distribution. Fechner proposed this procedure in his famous book Kollektivmaßlehre (1897), p. 295ff.. A similar proposal comes from...

It is well known that the arithmetic mean of two possibly different copulas forms a copula, again. More general, we focus on the weighted power mean (WPM) of two arbitrary copulas which is not necessary a copula again, as different counterexamples reveal. However, various conditions regarding...

Zhang (2008) defines the quotient correlation coefficient to test for dependence and tail dependence of bivariate random samples. He shows that asymptotically the test statistics are gamma distributed. Therefore, he called the corresponding test gamma test. We want to investigate the speed of...