In order to evaluate the quality of the scientific research, we introduce a new family of scientific performance measures, called Scientific Research Measures (SRM). Our proposal originates from the more recent developments in the theory of risk meas
ures and is an attempt to resolve the many problems of the existing bibliometric indices. The SRM that we introduce are based on the whole scientists citation record and are: coherent, as they share the same structural properties; flexible to fit peculiarities of different areas and seniorities; granular, as they allow a more precise comparison between scientists, and inclusive, as they comprehend several popular indices. Another key feature of our SRM is that they are planned to be calibrated to the particular scientific community. We also propose a dual formulation of this problem and explain its relevance in this context.
We propose a generalization of the classical notion of the $V@R_{lambda}$ that takes into account not only the probability of the losses, but the balance between such probability and the amount of the loss. This is obtained by defining a new class of
law invariant risk measures based on an appropriate family of acceptance sets. The $V@R_{lambda}$ and other known law invariant risk measures turn out to be special cases of our proposal. We further prove the dual representation of Risk Measures on $mathcal{P}(% mathbb{R}).$
