1. An oscilloscope for estimating a probability density function (PDF) for non-periodic, uncorrelated jitter comprising: control means operable to execute instructions for modifying a compound distribution representing acquired data that comprises non-periodic, uncorrelated jitter by: identifying low probability regions in the compound distribution; identifying a known approximation that models a distribution of at least a first portion of the low probability regions; removing the low probability regions; and replacing the removed low probability regions with the known approximation and an extrapolation of the known approximation; a user interface for activating signal impairment analysis, and for indicating when the analysis is completed; and a display unit for displaying the user interface.