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A critical examination is made of the relative merits of two techniques for testing for the exponential distribution, involving transformations of the original observations to random variables uniformly distributed on the null hypothesis.

Several types of multivariate extensions of the inverse Gaussian (IG) distribution and the reciprocal inverse Gaussian (RIG) distribution are proposed. Some of these types are obtained as random‐additive‐effect models by means of well‐known convolution properties of the IG and RIG distributions, and they have one‐dimensional IG or RIG marginals. They are used to define a flexible class of multivariate Poisson mixtures.