Dirichlet Integrals of Type 2 and Their Applications

This volume, edited by the Institute of Mathematical Statistics, deals with incomplete Dirichlet integrals of type 2 and is a companion book to Volume 4 of this series (by the same authors) which deals with incomplete Dirichlet integrals of type 1. As in the previous volume there are several new contributions present, some of which concern the development of new algorithms that made these tables possible, and there are many examples given to illustrate the use of the tables.Applications of these integrals are given to two types of problems: some that would be classified as being in the area of probability and some that are primarily statistical in nature. The probabilistic interpretation of the Dirichlet integral plays a major role in the direction taken and in the development of tables. An important area of application of these integrals is to ranking and selection problems dealing with the multinomial distribution, especially when the statistic of major interest is related to the minimum or maximum frequency among the cells and the stopping rule is of the type used in inverse sampling.
In the tables most attention is to the homogeneous multinomial; however much of the analysis attempts to get away from homogeneity.