Justification of probability density function for resolution in statistical models of overlap

Justification is offered for a postulate in a recent statistical model of overlap, which enabled theory to describe overlap in poorly resolved separations. In this model, resolutions of single-component peaks less than 0.5 were suggested to be sufficient for separation, although this suggestion obviously contradicted well established principles. Here, it is shown that the resolution of single-component peaks is a poor descriptor of overlap in inefficient separations. Rather, overlap is caused by the fusion of multiplets comprised of one or more single-component peaks, instead of single-component peaks. By relating the apparent resolution of multiplets to the actual resolution of their separated constituent single-component peaks, one can show that resolutions less than 0.5 can be sufficient for separation. A model is developed from these concepts to predict the probability density function for the resolution of single-component peaks at different efficiency. The combination of this probability density function with the recent statistical model of overlap correctly predicts overlap even when only one-fifth of the single-component peaks are detectable as observed maxima. The purpose of this work is not to propose a new statistical model of overlap but rather to justify the one noted above.