A regression characterization of inverse Gaussian distributionsand application to EDF goodness-of-fit tests

摘要

We give a new characterization of inverse Gaussian distributionsusing the regression of a suitable statistic based on a givenrandom sample. A corollary of this result is a characterizationof inverse Gaussian distribution based on a conditional jointdensity function of the sample. Application of this corollary asa transformation in the procedure to construct EDF (empiricaldistribution function) goodness-of-fit tests for inverse Gaussiandistributions is also studied.