The aim of this paper is to derive an index able to indicate if a discount function exhibits increasing or decreasing impatience, and, even, in the last case, whether the decreasing impatience is moderate or strong. Moreover, it will be shown that the sign of this indicator coincides with the sign of the convexity index of the discount function when only considering the cases of increasing and decreasing impatience. Consequently, this parameter supposes an improvement of Prelec's index of convexity. The main advantage of this novel measure is that, the same as Prelec's index, it uses the differential calculus and, moreover, can be easily plotted by showing the changes from a type of impatience to another one according to time.