C. Ittrich, D. Krause, W.-D. Richter
PROBABILITIES AND LARGE QUANTILES OF NONCENTRAL GENERALIZED CHI-SQUARE DISTRIBUTIONS
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

62E15 Exact distribution theory

62E17 Approximations to distributions (nonasymptotic)

Abstract: Exact values of probability integrals for noncentral
generalized chi-square distributions are numerically evaluated based upon
new geometric representation formulas for these distributions. Using
standard numerical methods exact quantiles can be calculated then.
Explicit quantile approximation formulas and algorithms are deduced from an
asymptotic expansion for related probabilities of large deviations. Several
numerical studies compare the present results with results of other
authors.

Keywords: spherical samples, geometric representation formulas, generalized chi-square distributions, exact distributions, exact quantiles, large quantiles, approximations, asymptotic expansions, large deviation quantile approximation