Error contours for Student's t under nonnormality

Geary (Biometrika 34, 1947) has introduced a differential series for the density function of Student's t under nonnormality where the sample population is assumed to have finite moments up to a certain order. If (K/sub r/) and (K'/sub r/) are the cumulants of t under the two regimes (normality and nonnormality), then the discrepancies (K/sub r/--K'/sub r/) can be ordered with respect to sample size, in an ordering in powers of 1/..sqrt..n(n = sample size) of the modified density and cumulative distribution function of t. Geary carried this out to order n/sup -2/. Relative error contours comparing Geary's n/sup -1/ and n/sup -2/ approximations of the upper and lower modified probability levels for ..cap alpha.. = 0.05 and n = 15, 20, and 25 are given for sets of mixtures of normal distributions, and Pearson distributions, in the (..sqrt beta../sub 1/,..beta../sub 2/) plane. Additional comparisons are given comparing these approximations from the results of a Monte Carlo simulation for a wide range of mixtures of normal distributions. 2 figures, 2 tables. (RWR