The inverse Gaussian distribution has been proposed as a model for distribution of life times. It is considered as an alternative to other observed distributions in particular to the lognormal. In this paper we consider a separate families of hypotheses test to detect departure from the inverse Gaussian in the direction of the lognormal, also considered is the case when the two hypotheses are changed, i.e. when it is required to test the departure from the lognormal in the direction of the inverse Gaussian. Comparison with a modified Kolmogorov-Smirnov test for the inverse Gaussian density is also considered