An Inductive Proof of the Sampling Distributions for the MLE's of the Parameters in an Inverse Gaussian Distribution

Tweedie showed that the sampling distributions of the MLE's for the parameters of an inverse Gaussian distribution were independent inverse Gaussian and chi-squared distributions.His proof, however, requires substantial mathematical machinery, for example, Laplace transforms, Lerch's theorem, or conditional moment generating functions.We present an inductive proof that only requires multivariable transformations that are presented in intermediate mathematical statistics classes.