Advances in Combinatorial Methods and Applications to Probability and Statistics

Sri Gopal Mohanty has made pioneering contributions to lattice path counting and its applications to probability and statistics. This is clearly evident from his lifetime publications list and the numerous citations his publications have received over the past three decades. My association with him began in 1982 when I came to McMaster Univer sity. Since then, I have been associated with him on many different issues at professional as well as cultural levels; I have benefited greatly from him on both these grounds. I have enjoyed very much being his colleague in the statistics group here at McMaster University and also as his friend. While I admire him for his honesty, sincerity and dedication, I appreciate very much his kindness, modesty and broad-mindedness. Aside from our common interest in mathematics and statistics, we both have great love for Indian classical music and dance. We have spent numerous many different subjects associated with the Indian music and hours discussing dance. I still remember fondly the long drive (to Amherst, Massachusetts) I had a few years ago with him and his wife, Shantimayee, and all the hearty discussions we had during that journey. Combinatorics and applications of combinatorial methods in probability and statistics has become a very active and fertile area of research in the recent past.

Texte du rabat
This volume presents 32 invited chapters by researchers in this field of mathematics. The goal of the book is to bring together the work of theoreticians and applied researchers and provide a broad forum to share ideas and recent results. The collection describes and surveys theoretical developments and demonstrates some important applications in a variety of areas, including: applications to queueing theory; waiting time problems; applications to distribution theory; and applications to nonparametric statistics.

Contenu
ILattice Paths and Combinatorial Methods.- 1 Lattice Paths and Faber Polynomials.- 2 Lattice Path Enumeration and Umbral Calculus.- 3 The Enumeration of Lattice Paths With Respect to Their Number of Turns.- 4 Lattice Path Counting Simple Random Walk Statistics, and Randomizations: An Analytic Approach.- 5 Combinatorial Identities: A Generalization of Dougall's Identity.- 6 A Comparison of Two Methods for Random Labelling of Balls by Vectors of Integers.- IIApplications to Probability Problems.- 7 On the Ballot Theorems.- 8 Some Results for Two-Dimensional Random Walk.- 9 Random Walks on SL(2, F2) and Jacobi Symbols of Quadratic Residues.- 10 Rank Order Statistics Related to a Generalized Random Walk.- 11 On a Subset Sum Algorithm and Its Probabilistic and Other Applications.- 12 I and J Polynomials in a Potpourri of Probability Problems.- 13 Stirling Numbers and Records.- IIIApplications to Urn Models.- 14 Advances in Urn Models During The Past Two Decades.- 15 A Unified Derivation of Occupancy and Sequential Occupancy Distributions.- 16 Moments Binomial Moments and Combinatorics.- IVApplications to Queueing Theory.- 17 Nonintersecting Paths and Applications to Queueing Theory.- 18 Transient Busy Period Analysis of Initially Non-Empty M/G/l QueuesLattice Path Approach.- 19 Single Server Queueing System with Poisson Input: A Review of Some Recent Developments.- 20 Recent Advances in the Analysis of Polling Systems.- VApplications to Waiting Time Problems.- 21 Waiting Times and Number of Appearances of Events in a Sequence of Discrete Random Variables.- 22 On Sooner and Later Problems Between Success and Failure Runs.- 23 Distributions of Numbers of Success-Runs Until the First Consecutive k Successes in Higher Order Markov Dependent Trials.- 24 OnMultivariate Distributions of Various Orders Obtained by Waiting for the r-th Success Run of Length k in Trials With Multiple Outcomes.- 25 A Multivariate Negative Binomial Distribution of Order k Arising When Success Runs are Allowed to Overlap.- VIApplications to Distribution Theory.- 26 The Joint Energy Distributions of the Bose-Einstein and of the Fermi-Dirac Particles.- 27 On Modified g-Bessel Functions and Some Statistical Applications.- 28 A g-Logarithmic Distribution.- 29 Bernoulli Learning Models: Uppuluri Numbers.- VIIApplications to Nonparametric Statistics.- 30 Linear Nonparametric Tests Against Restricted Alternatives: The Simple-Tree Order and The Simple Order.- 31 Nonparametric Estimation of the Ratio of Variance Components.- 32 Limit Theorems for M-Processes Via Rank Statistics Processes.- Author Index.