Overview

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.

Full Product Details

Author:   N. Balakrishnan
Publisher:   Birkhauser Boston Inc
Imprint:   Birkhauser Boston Inc
Edition:   1997 ed.
Dimensions:   Width: 17.80cm , Height: 3.30cm , Length: 25.40cm
Weight:   2.980kg
ISBN:  

9780817639082

ISBN 10:   081763908
Pages:   562
Publication Date:   01 May 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

I—Lattice 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.- II—Applications 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.- III—Applications 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.- IV—Applications to Queueing Theory.- 17 Nonintersecting Paths and Applications to Queueing Theory.- 18 Transient Busy Period Analysis of Initially Non-Empty M/G/l Queues—Lattice 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.- V—Applications 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.- VI—Applications 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.- VII—Applications 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.

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