Ebook: 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.

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Content:
Front Matter....Pages i-xxxiv
Front Matter....Pages 1-1
Lattice Paths and Faber Polynomials....Pages 3-13
Lattice Path Enumeration and Umbral Calculus....Pages 15-27
The Enumeration of Lattice Paths With Respect to Their Number of Turns....Pages 29-58
Lattice Path Counting, Simple Random Walk Statistics, and Randomization: An Analytic Approach....Pages 59-76
Combinatorial Identities: A Generalization of Dougall’s Identity....Pages 77-88
A Comparison Of Two Methods For Random Labelling of Balls by Vectors of Integers....Pages 89-93
Front Matter....Pages 95-95
On The Ballot Theorems....Pages 97-114
Some Results for Two-Dimensional Random Walk....Pages 115-124
Random Walks on SL(2, F2) and Jacobi Symbols of Quadratic Residues....Pages 125-134
Rank Order Statistics Related to a Generalized Random Walk....Pages 135-151
On a Subset Sum Algorithm and Its Probabilistic and Other Applications....Pages 153-163
I and J Polynomials in a Potpourri of Probability Problems....Pages 165-187
Stirling Numbers and Records....Pages 189-200
Front Matter....Pages 201-201
Advances in Urn Models during the Past Two Decades....Pages 203-257
Moments, Binomial Moments and Combinatorics....Pages 259-273
Front Matter....Pages 275-284
Nonintersecting Paths and Applications in Queueing Theory....Pages 285-285
Transient Busy Period Analysis of Initially Non-Empty M/G/l Queues—Lattice Path Approach....Pages 287-299
Single Server Queueing System with Poisson Input: A Review of Some Recent Developments....Pages 301-315
Recent Advances in the Analysis of Polling Systems....Pages 317-338
Front Matter....Pages 339-360
Waiting Times and Number of Appearances of Events in a Sequence of Discrete Random Variables....Pages 361-361
On Sooner and Later Problems Between Success and Failure Runs....Pages 363-384
Distributions of Numbers of Success-Runs Until the First Consecutive k Successes in Higher Order Markov Dependent Trials....Pages 385-400
On Multivariate Distributions of Various Orders Obtained by Waiting for the r-th Success Run of Length k in Trials With Multiple Outcomes....Pages 401-410
A Multivariate Negative Binomial Distribution of Order k Arising When Success Runs are Allowed to Overlap....Pages 411-426
Front Matter....Pages 427-438
The Joint Energy Distributions of the Bose-Einstein and of the Fermi-Dirac Particles....Pages 439-439
On Modified q-Bessel Functions and Some Statistical Applications....Pages 441-449
A q-Logarithmic Distribution....Pages 451-463
Bernoulli Learning Models: Uppuluri Numbers....Pages 465-470
Front Matter....Pages 471-480
Linear Nonparametric Tests Against Restricted Alternatives: The Simple-Tree Order and The Simple Order....Pages 481-481
Nonparametric Estimation of the Ratio of Variance Components....Pages 483-506
Limit Theorems for M-Processes Via Rank Statistics Processes....Pages 507-519
Back Matter....Pages 521-534
....Pages 535-562