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Keywords:
generalized $p$-value; inversion formula; Behrens-Fisher problem
generalized $p$-value; inversion formula; Behrens-Fisher problem
Summary:
A formula for evaluation of the distribution of a linear combination of independent inverted gamma random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil–Pelaez [gil-pelaez]. This method is applied to computation of the generalized $p$-values used for exact significance testing and interval estimation of the parameter of interest in the Behrens–Fisher problem and for variance components in balanced mixed linear model.
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