Evaluation and applications of the multivariate normal distribution with a singular negative product correlation structure

The dissertation presents a new theorem, alternative to the existing theorems, for evaluating the one-sided exact percentage points of an m-variate normal distribution with a singular negative product correlation structure and also provides a new approach to evaluate the two-sided cases for small m. The results are then applied to the asymptotic multinomial distribution for constructing joint simultaneous confidence intervals for the multinomial proportions and also for estimating sample sizes. By extending the results from the multivariate normal distribution to the multivariate t-distribution with corresponding singular correlation structure, we tabulate the one-sided and two-sided critical points for the Analysis of Means (ANOM) procedure. Simple approximations to the exact one-sided and two-sided critical points for ANOM with unequal sample sizes are also proposed.