Advances in Combinatorial Methods and Applications to Probability and Statistics / Edition 1

Advances in Combinatorial Methods and Applications to Probability and Statistics / Edition 1

by N. Balakrishnan

ISBN-10: 081763908X

ISBN-13: 9780817639082

Pub. Date: 05/01/1997

Publisher: Birkhauser Verlag

Product Details

Birkhauser Verlag
Publication date:
Statistics for Industry and Technology Series
Edition description:
Product dimensions:
10.00(w) x 7.00(h) x 1.31(d)

Table of Contents

Sri Gopal Mohanty - Life and Works
List of Contributors
List of Tables
List of Figures
1Lattice Paths and Faber Polynomials3
2Lattice Path Enumeration and Umbral Calculus15
3The Enumeration of Lattice Paths With Respect to Their Number of Turns29
4Lattice Path Counting, Simple Random Walk Statistics, and Randomizations: An Analytic Approach59
5Combinatorial Identities: A Generalization of Dougall's Identity77
6A Comparison of Two Methods for Random Labelling of Balls by Vectors of Integers89
7On the Ballot Theorems97
8Some Results for Two-Dimensional Random Walk115
9Random Walks on SL(2, F[subscript 2]) and Jacobi Symbols of Quadratic Residues125
10Rank Order Statistics Related to a Generalized Random Walk135
11On a Subset Sum Algorithm and Its Probabilistic and Other Applications153
12I and J Polynomials in Potpourri of Probability Problems165
13Stirling Numbers and Records189
14Advances in Urn Models During The Past Two Decades203
15A Unified Derivation of Occupancy and Sequential Occupancy Distributions259
16Moments, Binomial Moments and Combinatorics275
17Nonintersecting Paths and Applications to Queueing Theory287
18Transient Busy Period Analysis of Initially Non-Empty M/G/1 Queues - Lattice Path Approach301
19Single Server Queueing System with Poisson Input: A Review of Some Recent Developments317
20Recent Advances in the Analysis of Polling Systems339
21Waiting Times and Number of Appearances of Events in a Sequence of Discrete Random Variables363
22On Sooner and Later Problems Between Success and Failure Runs385
23Distributions of Numbers of Success-Runs Until the First Consecutive k Successes in Higher Order Markov Dependent Trials401
24On Multivariate Distributions of Various Orders Obtained by Waiting for the r-th Success Run of Length k in Trials With Multiple Outcomes411
25A Multivariate Negative Binomial Distribution of Order k Arising When Success Runs are Allowed to Overlap427
26The Joint Energy Distributions of the Bose-Einstein and of the Fermi-Dirac Particles441
27On Modified q-Bessel Functions and Some Statistical Applications451
28A q-Logarithmic Distribution465
29Bernoulli Learning Models: Uppuluri Numbers471
30Linear Nonparametric Tests Against Restricted Alternatives: The Simple-Tree Order and The Simple Order483
31Nonparametric Estimation of the Ratio of Variance Components507
32Limit Theorems for M-Processes Via Rank Statistics Processes521
Author Index535
Subject Index545

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