Output distributional influence function

When a filter is being selected for an application, it is often essential t o know that the behavior of the filter does not change significantly if the re are small deviations from the initial assumptions. This robustness of a filter is traditionally explored by means of influence function (IF) and ch ange-of-variance function (CVF). However, as these are asymptotic measures, there is uncertainty of the applicability of the obtained results to the f inite-length filters used in the real-world filtering applications. In this paper, we present a new method called the output distributional influence function (ODIF) that examines the robustness of the finite-length filters. The method gives most extensive information about the robustness for filter s with a known output distribution function. As examples, the ODIFs for the distribution function, density function, expectation, and variance are giv en for the well-known mean and median filters and are interpreted in detail .