The framework of this paper is behavioral finance and, more specifically, intertemporal choice when individuals exhibit decreasing impatience in their decision-making processes. After characterizing the two main types of decreasing impatience (moderately and strongly decreasing impatience), the main objective of this paper is to generalize these concepts when the criterion of time increase is given by an arbitrary function which describes such increments. In general, the methodology is mathematical calculus but particularly the concept of derivative according to the function which rules the increase of time. The main contribution of this paper is the characterization of this extension of the concept of decreasing impatience by using the aforementioned novel derivative and the well-known Prelec's index.