This chapter is devoted to tests of hypotheses for parameters of IG(µ,λ). We derive the likelihood ratio tests for the mean parameter as well as the lambda parameter in the one and two sample cases; we also consider tests for the Brownian motion process. The power of these tests is examined briefly.We study interval estimation from both the frquentist as well as the Bayesian points of view. Prediction intervals and tolerance limits are examined in detail and numerous illustrative examples are provided. A section is devoted to tests of separate families first considered by Cox (1961) and we illustrate this with applications to simulated and physiological data to test inverse Gaussian against the lognormal and vice versa. Finally we discuss Bahadur efficient tests.
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