An alternative approach to measurement based on quantile functions

In many fields of science and engineering the correct choice of the observation domain may facilitate the study of a phenomenon. Various measurement activities are traditionally based on the concepts of probability density and cumulative distribution functions. However, the conversion of such activities to the quantile domain offers several theoretical and practical advantages and introduces a sort of alternative statistical universe in which the quantile functions are the fundamental objects. Even though it is possible to pass from an universe to the other, these two universes have different strengths and weaknesses that will be investigated in this paper with emphasis on measurement applications.