n. 1. (Statistics) the set of possible values of a random variable, or points in a sample space, considered in terms of their theoretical or observed frequency. 2. also called generalized function. a generalization of the concept of a function, defined as continuous linear functionals over spaces of infinitely differentiable functions, introduced so that all continuous functions possess partial distributional derivatives (also called Schwartzian derivatives) that are again distributions. This leads to so-called weak solutions of differential equations and is of importance in the theory of partial differential equations.