Asymptotic expansions for the distribution of quadratic forms in normal variables (original) (raw)

Higher order asymptotic expansions for the distribution of quadratic forms in normal variables are obtained. The Cornish-Fisher inverse expansions for the percentiles of the distribution are also given. The tesulting formula for a definite quadratic form guarantees accuracy almost up to fourth decimal place if the distribution is not very skew. The normalizing transformation investigated by Jensen and Solomon (1972, J. Amer. Statist. Assoc., 67, 898-902) is reconsidered based on the rate of convergence to the normal distribution.