  We propose novel goodness-of-fit tests for the Weibull distribution with
unknown parameters. These tests are based on an alternative characterizing
representation of the Laplace transform related to the density approach in the
context of Stein's method. Asymptotic theory of the tests is derived, including
the limit null distribution, the behaviour under contiguous alternatives, the
validity of the parametric bootstrap procedure, and consistency of the tests
against a large class of alternatives. A Monte Carlo simulation study shows the
competitiveness of the new procedure. Finally, the procedure is applied to real
data examples taken from the materials science.
