We consider m distributions where the first m-1 are obtained by multiplicative exponential distortions of the the mth distribution, it being a reference. Given m corresponding samples, the semiparametric large sample problem is worked out regarding the estimation from the combined data of each distortion and the common factor, and testing the hypothesis the distributions are identical. The approach is a generalization of the classical one way layout classification in the general sense it obviates the need for a complete specified parametric model. An advantage is that the common factor, the probability density of the mth distribution, is estimated from the combined data and not just from the $m$th sample. A power comparison with the t and F tests obtained by simulation points to the merit of the present approach. The method is applied to rain rate data from meteorological instruments.