Error analysis of parameters determined with statistical models of overlap from nonhomogeneous separations

The origin of uncertainties in the number of peaks in analytical separations predicted by statistical models of overlap is reviewed. An expression for the variance of the number of peaks in separations containing nonhomogeneous Poisson distributions of single-component peaks is then derived. This expression is confirmed by simple computer simulations of nonhomogeneous Poisson point processes. The expression is used to calculate the uncertainty in the estimate of the number of single-component peaks in, and saturations of, 48 gas chromatograms of lime oil. An expression derived by Martin and coworkers for the probability density function of single-component peaks also is modified by an estimate of the number of single-component peaks to reduce the functionʹs breadth and to improve the statistical parameters calculated from the function.