Lattice Path Combinatorics with Statistical Applications; Mathematical Expositions 23 / / T.V. Narayana.

• Superior document: Title is part of eBook package: De Gruyter University of Toronto Press eBook-Package Archive 1933-1999
• VerfasserIn: Narayana, T.V.,
• Place / Publishing House: Toronto : : University of Toronto Press, , [2019]; ©1979
• Year of Publication: 2019
• Language: English
• Series: Heritage
• Physical Description: 1 online resource (120 p.)

Lattice path combinatorics has developed greatly as a branch of probability studies recently, and the need for new books on the subject is obvious. The present monograph, by one who has made significant contributions to combinatorics and its applications to probability and statistics, will be useful to research workers, teachers, professional statisticians, and advanced students alike. It treats several recent results and it offers a powerful new tool for studying many problems in mathematical statistics. The emphasis in the five chapters is on 'dominance.' From a consideration of exceedances in the lattice path problem, the text goes on to provide solutions to tests of hypotheses and simple sampling plans, displaying the usefulness of Young chains in the enumeration of the latter. The fourth chapter, on knock-out tournaments, represents one approach to paired comparisons quite close in spirit to dominance and lattice path combinatorics, and the final chapter considers the advantages of using combinatorial methods in statistical problems (including the Frame-Robinson-Thrall theorem to derive properties of non-parametric tests) and mentions current trends of research. Numerous examples, exercises, and references round out the text.

Table of Contents

Frontmatter -- Contents -- Tables -- Preface -- LATTICE PATH COMBINATORICS WITH STATISTICAL APPLICATIONS -- I. Lattice path problems and vectors of integers -- II. The dominance theorem and Smirnov test-statistics -- III. Some applications of dominance to statistical problems -- IV. The combinatorics of knock-out tournaments -- V. A miscellany of further research problems -- APPENDIX -- REFERENCES -- Notes and solutions -- Supplementary bibliography -- Index