Finite-sample distributions of self-normalized sums

Logan et al. (1973) analyze the limit probability distribution of the statistic sn(p) = Σi=1 Xi/(Σi=1 | Χj |^p)^1/p as n → ∞, when Xi is in the domain of attraciton of a stable law with stabilility index α. By simulations, we provide quantiles of the usual critical levels of the finite-sample distributions of the Student?s t-statistic as α tξ(n) = Sn (p) [(n −1) / (n − Sn^2(p))]^1/2 with p = 2 . The response surface method is used to provide approximate quantiles of the finite-sample distributions of the Student's t-statistic.