Output distributional influence function

When a filter is being selected for an application, it is often essential to know that the behavior of the filter does not change significantly if there are small deviations from the initial assumptions. This robustness of a filter is traditionally explored by means of the influence function (IF) and change-of-variance function (CVF). However, as these are asymptotic measures, there is uncertainty of the applicability of the obtained results to the finite-length filters used in the real-world filtering applications. 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 filters with a known output distribution function. As examples, the ODIFs for the distribution function, density function, expectation, and variance are given for the well-known mean and median filters and are interpreted in detail.