Estimating distribution functions in Johnson translation system by the starship procedure with simulated annealing

The computer intensive starship procedure by Owen allows to obtain the best transformation to normality using the global optimization of some measure of non-normality. In this paper, we propose to apply the procedure to estimate a cumulative distribution function in the Johnson translation system by means of the optimization of sampling statistics derived by the minimum distance and non-linear least squares methods. As global optimization method we consider a stochastic optimization method, specifically the simulated annealing, as an alternative to the method proposed by Owen and Li which is based on the Slifker and Shapiro criterion. The application of the starship procedure to a simulated sample shows that the simulated annealing algorithm inserted in the procedure supplies results better than the results obtained with the Slifker and Shapiro criterion. Moreover the problems of convergence that occur with traditional optimization methods are not present.