A probability inequality for ranges and its application to maximum range test procedures

Summary It is proved that for any fixed argument the sequence (P _k) of the distribution functions of the ranges ofk i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of “log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all pairwise comparisons (Royen 1988, 1989a, 1989b). Under the above assumptions the application of this algorithm can be extended e.g. to pairwise comparisons of variances.     

Interpretive structural modeling—A useful tool for technology assessment?

Interpretive Structural Modeling (ISM) is a computer based technique for helping small groups develop graphical representations of complex systems. In this paper, the rationale for the use of Interpretative Structural Modeling in activities such as technology assessment is developed and the basic concepts underlying the technique are explored. Several applications of ISM are described and from these experiences some observations are made about the nature and effectiveness of the ISM process and product. ISM was found to provide its users with a systematic and comprehensive method for integrating group judgments in the development of “first-cut‘ structural models. At the same time, however, the technique was found to be relatively inflexible and may, in some instances, inhibit group processes. Possible directions for the development of less rigid methods are suggested.     

Über die Existenz einer stetigen,reellenNutzenfunktion

Ohne ZusammenfassungHerrn Prof. J. Nitsche (Freiburg) danke ich für die kritische Durchsicht einer ersten Fassung des Manuskriptes, ebenso danke ich Prof. Robert Reichardt (Wien) für einige kritische Anmerkungen. Für mögliche Fehler bleibe ich jedoch allein verantwortlich.