We are developing a new approach to this problem, exploiting the fact that the salient non-Gaussian features of the observed distributions are well captured by a general class of so-called Stochastically Generated Skewed (SGS) distributions that include Gaussian distributions as special cases. SGS distributions are associated with damped linear Markov processes perturbed by asymmetric stochastic noise, and as such represent the simplest physically based prototypes of the observed distributions. The tails of SGS distributions can also be directly linked to Generalized Extreme Value (GEV) and Generalized Pareto (GP) distributions. These tails are, however, more accurately estimated using all available data instead of just extreme values as in the standard GEV or GP approaches. The Markov process model can be used to provide rigorous confidence intervals, and to investigate temporal persistence statistics. In this talk, we will illustrate the procedure for assessing changes in the observed distributions of daily wintertime indices of large-scale atmospheric variability in the North Atlantic and North Pacific sectors over the 1872-2011 period. No significant changes in these indices were found from the first half to the second half of the period.