Hayakawa (1990) has very recently studied the behavior of the power for several large sample tests for the mean direction vector of the Langevin distribution. These tests are not known to possess any non-trivial optimal property. Here we derive some multiparameter locally optimal tests, e.g.,...

B. Mandelbrot and E. Fama in the sixties, and W. Ziemba in the seventies, suggested stable laws for modeling stock returns and commodity prices. Geometric stable distributions, with Laplace distribution playing the role of a "normal" law, have been found to give better fit to such data. We study...