STATISTICAL-THEORY OF OVERLAP FOR VARIABLE POISSON DENSITY - RELAXATION OF CONSTRAINT OF RANDOMNESS

The statistical model of overlap is modified to address one-dimensional separations containing single-component peaks (SCPs) with variable Poisson densities. The resulting theory describes overlap in unsaturated separations, for which the variation of SCP density throughout the separation is known. The expected number of peaks is expressed by an integral, whose value depends on the average saturation of the separation, the number of detectable components, and a frequency function proportional to the SCP density. The theory is verified by its application to computer-simulated chromatograms containing SCPs with linear, quadratic, sinusoidal, and exponential frequencies. Procedures are proposed to estimate the frequency function from the distribution of chromatographic maxima. and to estimate the number of detectable components in chromatograms. These procedures are verified by their application to computer-simulated chromatograms and to an experimental chromatogram of a well-characterized mixture. Computer simulations show that these procedures are more robust than those based on a constant Poisson density. A mathematical proof is offered, which shows that at constant low average saturation the maximum number of peaks:ln a separation containing SCPs with variable Poisson densities is obtained, when the SCP density is constant. This proof may explain previous experimental observations.