Least Squares for Generalized Gauss–Laplace Distribution of the Error in Certain Nonlinear Regressions with Perpendicular Offsets

There are mainly two methods of calculating the parameters of the regression equations: the minimization of the squared errors (or least squares, LS) and the maximization of the likelihood. Regarding the distribution of the error of experimental observations, there are several theoretical distributions, but two of them are on the one hand better known and on the other easily generalizable into one (Gauss–Laplace, GL): the normal (or Gaussian) distribution and the double exponential (or Laplace) distribution. In the construction of the squared errors is possible to replace the classical vertical offsets (which are the sides of the squares of the errors) with perpendicular ones, more suited when all variables are equally subjected to experimental errors. In the present work, it is proposed to use an iterative algorithm for the calculation of the regression parameters using LS of perpendicular offsets under the assumption of GL distributed error. The method is exemplified on a non-linear regression model.