Error bounds for asymptotic expansions of scale mixtures of distributions (Q1122253)

The author has considered the distribution of a scale mixture \(X=\sigma Z\) of a random variable Z which has a general distribution, with the scale factor \(\sigma >0\). By expanding the conditional distribution function of X for a given \(\sigma\) in a Taylor series in \(\sigma^{-1}- 1\), an asymptotic expansion of F(x), the distribution function of X, and its error bound have been obtained. The problems are reduced to the case when Z is distributed as N(0,1) and a chi-square distribution. The general theory has been successfully applied to derive expansions of t- distributions and F-distributions.