*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.*

Skip to content
# 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.
# Advances in Combinatorial Methods and Applications to Probability and Statistics

# Statistical Advances in Biosciences and Bioinformatics

Papers presented at the conference, held during 23-27 Nov. 2003, at Banaras Hindu University, Varanasi.
# Probability and Statistical Models with Applications

This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probability and Statistical Models with Applications is a must read for probabilists and theoretical and applied statisticians.
# Runs and Scans with Applications

Expert practical and theoretical coverage of runs and scans This volume presents both theoretical and applied aspects of runsand scans, and illustrates their important role in reliabilityanalysis through various applications from science and engineering.Runs and Scans with Applications presents new and exciting contentin a systematic and cohesive way in a single comprehensive volume,complete with relevant approximations and explanations of somelimit theorems. The authors provide detailed discussions of both classical andcurrent problems, such as: * Sooner and later waiting time * Consecutive systems * Start-up demonstration testing in life-testing experiments * Learning and memory models * "Match" in genetic codes Runs and Scans with Applications offers broad coverage of thesubject in the context of reliability and life-testing settings andserves as an authoritative reference for students and professionalsalike.
# Combinatorial Methods in Discrete Distributions

A unique approach illustrating discrete distribution theory throughcombinatorial methods This book provides a unique approach by presenting combinatorialmethods in tandem with discrete distribution theory. This method,particular to discreteness, allows readers to gain a deeperunderstanding of theory by using applications to solve problems.The author makes extensive use of the reduction approach toconditional distributions of independent random occupancy numbers,and provides excellent studies of occupancy and sequentialoccupancy distributions, convolutions of truncated discretedistributions, and compound and mixture distributions. Combinatorial Methods in Discrete Distributions begins with abrief presentation of set theory followed by basic countingprinciples. Fundamental principles of combinatorics, finitedifferences, and discrete probability are included to give readersthe necessary foundation to the topics presented in the text. A thorough examination of the field is provided andfeatures: Stirling numbers and generalized factorial coefficients Occupancy and sequential occupancy distributions n-fold convolutions of truncated distributions Compound and mixture distributions Thoroughly worked examples aid readers in understanding complextheory and discovering how theory can be applied to solve practicalproblems. An appendix with hints and answers to the exercises helpsreaders work through the more complex sections. Reference notes areprovided at the end of each chapter, and an extensive bibliographyoffers readers a resource for additional information on specializedtopics.
# Foundations of Statistical Analyses and Applications with SAS

This book links up the theory of a selection of statistical procedures used in general practice with their application to real world data sets using the statistical software package SAS (Statistical Analysis System). These applications are intended to illustrate the theory and to provide, simultaneously, the ability to use the knowledge effectively and readily in execution.
# Advances in Distribution Theory Order Statistics and Inference

The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.
# Statistical Data Analysis Based on the L1 Norm and Related Methods

This volume contains a selection of invited papers, presented to the fourth International Conference on Statistical Data Analysis Based on the L1-Norm and Related Methods, held in Neuchâtel, Switzerland, from August 4–9, 2002. The contributions represent clear evidence to the importance of the development of theory, methods and applications related to the statistical data analysis based on the L1-norm.
# Mathematical and Statistical Methods in Reliability

This book contains extended versions of 34 carefully selected and reviewed papers presented at the Third International Conference on Mathematical Methods in Reliability, held in Trondheim, Norway in 2002. It provides a broad overview of current research activities in reliability theory and its applications. There are chapters on reliability modelling, network and system reliability, reliability optimization, survival analysis, degradation and maintenance modelling, and software reliability. The authors are all leading experts in the field. A particular feature of the book is a historical review by Professor Richard E Barlow, well known for his pioneering research on reliability. The list of authors also includes the plenary session speakers Odd O Aalen, Philip J Boland, Sallie A Keller-McNulty, and Nozer Singpurwalla. Contents:Reliability Theory in the Past and Present CenturiesGeneral Aspects of Reliability ModellingReliability of Networks and SystemsStochastic Modelling and Optimization in ReliabilityModelling in Survival and Reliability AnalysisStatistical Methods for Degradation DataStatistical Methods for Maintained SystemsStatistical Inference in Survival AnalysisSoftware Reliability Methods Readership: Graduate students, academics and professionals in probability & statistics, reliability analysis, survival analysis, industrial engineering, software engineering, operations research and applied mathematics research. Keywords:Applied Probability;Bayesian Analysis;Maintenance Modeling;Reliability Theory;Software Reliability;Statistical Inference;Survival Analysis
# Lattice Path Combinatorics and Applications

The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume. Contributions to this edited volume will be mainly research articles however it will also include several captivating, expository articles (along with pictures) on the life and mathematical work of leading researchers in lattice path combinatorics and beyond. There will be four or five expository articles in memory of Shreeram Shankar Abhyankar and Philippe Flajolet and honoring George Andrews and Lajos Takács. There may be another brief article in memory of Professors Jagdish Narayan Srivastava and Joti Lal Jain. New research results include the kernel method developed by Flajolet and others for counting different classes of lattice paths continues to produce new results in counting lattice paths. The recent investigation of Fishburn numbers has led to interesting counting interpretations and a family of fascinating congruences. Formulas for new methods to obtain the number of Fq-rational points of Schubert varieties in Grassmannians continues to have research interest and will be presented here. Topics to be included are far reaching and will include lattice path enumeration, tilings, bijections between paths and other combinatoric structures, non-intersecting lattice paths, varieties, Young tableaux, partitions, enumerative combinatorics, discrete distributions, applications to queueing theory and other continuous time models, graph theory and applications. Many leading mathematicians who spoke at the conference from which this volume derives, are expected to send contributions including. This volume also presents the stimulating ideas of some exciting newcomers to the Lattice Path Combinatorics Conference series; “The 8th Conference on Lattice Path Combinatorics and Applications” provided opportunities for new collaborations; some of the products of these collaborations will also appear in this book. This book will have interest for researchers in lattice path combinatorics and enumerative combinatorics. This will include subsets of researchers in mathematics, statistics, operations research and computer science. The applications of the material covered in this edited volume extends beyond the primary audience to scholars interested queuing theory, graph theory, tiling, partitions, distributions, etc. An attractive bonus within our book is the collection of special articles describing the top recent researchers in this area of study and documenting the interesting history of who, when and how these beautiful combinatorial results were originally discovered.
# Scan Statistics and Applications

The study of scan statistics and their applications to many different scientific and engineering problems have received considerable attention in the literature recently. In addition to challenging theoretical problems, the area of scan statis tics has also found exciting applications in diverse disciplines such as archaeol ogy, astronomy, epidemiology, geography, material science, molecular biology, reconnaissance, reliability and quality control, sociology, and telecommunica tion. This will be clearly evident when one goes through this volume. In this volume, we have brought together a collection of experts working in this area of research in order to review some of the developments that have taken place over the years and also to present their new works and point out some open problems. With this in mind, we selected authors for this volume with some having theoretical interests and others being primarily concerned with applications of scan statistics. Our sincere hope is that this volume will thus provide a comprehensive survey of all the developments in this area of research and hence will serve as a valuable source as well as reference for theoreticians and applied researchers. Graduate students interested in this area will find this volume to be particularly useful as it points out many open challenging problems that they could pursue. This volume will also be appropriate for teaching a graduate-level special course on this topic.
# Distribution Theory of Runs and Patterns and Its Applications

This book provides a rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics. The central theme of this approach is to properly imbed the random variables of interest into the framework of a finite Markov chain, and the resulting representations of the underlying distributions are compact and very amenable to further study of associated properties. The concept of finite Markov chain imbedding is systematically developed, and its utility is illustrated through practical applications to a variety of fields, including the reliability of engineering systems, hypothesis testing, quality control, and continuity measurement in the health care sector. Contents: Finite Markov Chain Imbedding; Runs and Patterns in a Sequence of Two-State Trials; Runs and Patterns in Multi-State Trials; Waiting-Time Distributions; Random Permutations; Applications. Readership: Graduate students and researchers in probability and statistics.
# Characterizations of Univariate Continuous Distributions

Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.
# Probability Statistics and Stochastic Processes for Engineers and Scientists

Featuring recent advances in the field, this new textbook presents probability and statistics, and their applications in stochastic processes. This book presents key information for understanding the essential aspects of basic probability theory and concepts of reliability as an application. The purpose of this book is to provide an option in this field that combines these areas in one book, balances both theory and practical applications, and also keeps the practitioners in mind. Features Includes numerous examples using current technologies with applications in various fields of study Offers many practical applications of probability in queueing models, all of which are related to the appropriate stochastic processes (continuous time such as waiting time, and fuzzy and discrete time like the classic Gambler’s Ruin Problem) Presents different current topics like probability distributions used in real-world applications of statistics such as climate control and pollution Different types of computer software such as MATLAB®, Minitab, MS Excel, and R as options for illustration, programing and calculation purposes and data analysis Covers reliability and its application in network queues
# Extreme Value Distributions

The aim of the book is to give a through account of the basic theory of extreme value distributions. The book cover a wide range of materials available to date. The central ideas and results of extreme value distributions are presented. The book rwill be useful o applied statisticians as well statisticians interrested to work in the area of extremen value distributions.vmonograph presents the central ideas and results of extreme value distributions.The monograph gives self-contained of theory and applications of extreme value distributions.
# Combinatorial Mathematics

This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics. The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments. Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science. Optional more advanced material also makes it valuable as a research reference. Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material. It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty. Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language. The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.
# Univariate Discrete Distributions

This Set Contains: Continuous Multivariate Distributions, Volume 1, Models andApplications, 2nd Edition by Samuel Kotz, N. Balakrishnan andNormal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Editionby Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Editionby Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N.Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by SamuelKotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributionstheory The Third Edition of the critically acclaimedUnivariate Discrete Distributions provides a self-contained,systematic treatment of the theory, derivation, and application ofprobability distributions for count data. Generalized zeta-functionand q-series distributions have been added and are covered indetail. New families of distributions, including Lagrangian-typedistributions, are integrated into this thoroughly revised andupdated text. Additional applications of univariate discretedistributions are explored to demonstrate the flexibility of thispowerful method. A thorough survey of recent statistical literature drawsattention to many new distributions and results for the classicaldistributions. Approximately 450 new references along with severalnew sections are introduced to reflect the current literature andknowledge of discrete distributions. Beginning with mathematical, probability, and statisticalfundamentals, the authors provide clear coverage of the key topicsin the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance ofBayesian inference to discrete distribution, especially with regardto the binomial and Poisson distributions. New derivations ofdiscrete distributions via stochastic processes and random walksare introduced without unnecessarily complex discussions ofstochastic processes. Throughout the Third Edition, extensiveinformation has been added to reflect the new role ofcomputer-based applications. With its thorough coverage and balanced presentation of theoryand application, this is an excellent and essential reference forstatisticians and mathematicians.
# Horizons of Combinatorics

Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives an overview of recent trends and results in a large part of combinatorics and related topics.
# DNA Words and Models

Publisher Description