Sharma and Autar [6] have formed a functional equation in two variables containing two parameters which, as a particular case, includes Daróczy's [1] generalized functional equation used in information theory. The solutions of our functional equation, under suitable boundary conditions, lead to an inaccuracy function of a new type. A characterization of this inaccuracy function and the convexity of Daróczy's entropy of type-ß have been given in this paper.