| Abstract | In this paper the exact distribution of the logarithm of the likelihood ratio test (l.r.t.) statistic for testing circular symmetry is obtained, for an odd number of variables p, in the form of a Generalized Integer Gamma distribution and, for an even p, in the form of an infinite mixture of Generalized Near-Integer Gamma distributions. For the case of an even p, two kinds of near-exact distributions are developed for the likelihood ratio test statistic which correspond, for the logarithm of the l.r.t. statistic, to a Generalized Near-Integer Gamma distribution or finite mixtures of these distributions. Numerical studies are conducted in order to assess the quality of these new approximations. Tables of exact quantiles, for odd p, and near-exact quantiles, for even p are presented. |
