Least squares fitting of the lognormal curve

Problems arising in nonlinear least squares fitting of the first part of the lognormal curve to data are analysed. No evidence of the existence of multiple local minima of the sum of squares has been found. However, it is demonstrated that severe convergence problems might arise, especially if the data points do not indicate the point of inflexion. This is caused by the fact that for small values of the running variable in the lognormal formula with respect to the localisation parameter, the lognormal curve with three parameters can be approximated closely by the exponential curve with two parameters.