Advances in Combinatorial Methods and Applications to Probability and Statistics

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, F 2 ) 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
 A Unified Derivation of Occupancy and Sequential Occupancy Distributions ....Pages 259-273
Moments, Binomial Moments and Combinatorics....Pages 275-284
Front Matter....Pages 285-285
Nonintersecting Paths and Applications in Queueing Theory....Pages 287-299
Transient Busy Period Analysis of Initially Non-Empty M/G/l Queues—Lattice Path Approach....Pages 301-315
Single Server Queueing System with Poisson Input: A Review of Some Recent Developments....Pages 317-338
Recent Advances in the Analysis of Polling Systems....Pages 339-360
Front Matter....Pages 361-361
Waiting Times and Number of Appearances of Events in a Sequence of Discrete Random Variables....Pages 363-384
On Sooner and Later Problems Between Success and Failure Runs....Pages 385-400
Distributions of Numbers of Success-Runs Until the First Consecutive k Successes in Higher Order Markov Dependent Trials....Pages 401-410
On Multivariate Distributions of Various Orders Obtained by Waiting for the r-th Success Run of Length k in Trials With Multiple Outcomes....Pages 411-426
A Multivariate Negative Binomial Distribution of Order k Arising When Success Runs are Allowed to Overlap....Pages 427-438
Front Matter....Pages 439-439
The Joint Energy Distributions of the Bose-Einstein and of the Fermi-Dirac Particles....Pages 441-449
On Modified q-Bessel Functions and Some Statistical Applications....Pages 451-463
A q-Logarithmic Distribution....Pages 465-470
Bernoulli Learning Models: Uppuluri Numbers....Pages 471-480
Front Matter....Pages 481-481
Linear Nonparametric Tests Against Restricted Alternatives: The Simple-Tree Order and The Simple Order....Pages 483-506
Nonparametric Estimation of the Ratio of Variance Components....Pages 507-519
Limit Theorems for M-Processes Via Rank Statistics Processes....Pages 521-534
Back Matter....Pages 535-562