Author : James C. Fu
Publisher : World Scientific
Page : 174 pages
File Size : 40,4 MB
Release : 2003
Category : Mathematics
ISBN : 9810245874
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.
Author : James C. Fu
Publisher : World Scientific
Page : 176 pages
File Size : 35,5 MB
Release : 2003-01-01
Category : Mathematics
ISBN : 9789812779205
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.
Author : James C. Fu
Publisher :
Page : pages
File Size : 49,74 MB
Release : 2003
Category : Distribution (Probability theory)
ISBN :
Author : Anant P. Godbole
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 19,38 MB
Release : 1994-04-30
Category : Mathematics
ISBN : 9780792328346
The Probability Theory of Patterns and Runs has had a long and distinguished history, starting with the work of de Moivre in the 18th century and that of von Mises in the early 1920's, and continuing with the renewal-theoretic results in Feller's classic text An Introduction to Probability Theory and its Applications, Volume 1. It is worthwhile to note, in particular, that de Moivre, in the third edition of The Doctrine of Chances (1756, reprinted by Chelsea in 1967, pp. 254-259), provides the generating function for the waiting time for the appearance of k consecutive successes. During the 1940's, statisticians such as Mood, Wolfowitz, David and Mosteller studied the distribution theory, both exact and asymptotic, of run-related statistics, thereby laying the foundation for several exact run tests. In the last two decades or so, the theory has seen an impressive re-emergence, primarily due to important developments in Molecular Biology, but also due to related research thrusts in Reliability Theory, Distribution Theory, Combinatorics, and Statistics.
Author : R. S. Pathak
Publisher : Alpha Science Int'l Ltd.
Page : 162 pages
File Size : 18,77 MB
Release : 2001
Category : Mathematics
ISBN : 9781842650202
Provides basic ideas and results of distribution theory and its applications to Fourier analysis and partial differential equations. Examples are provided to illustrate the concepts; exercises of various level of difficulty are given. Important topics covered like basic properties of distributions, convolution, Fourier transforms, Sobolev spaces, weak solutions, distributions on locally convex spaces and on differentiable manifolds.
Author : Fozia Homa
Publisher :
Page : 0 pages
File Size : 49,36 MB
Release : 2023
Category : MATHEMATICS
ISBN : 9781000779202
"This book aims to provide a thorough understanding of distribution theory and data analysis using statistical software to solve problems related to basic statistics, probability models, and simulation. The volume provides a detailed concept of different distributions used in statistics with their application in real-life situations. Covering the analytical aspects using the latest software, the volume discusses stochastic methods and other statistical methods. It provides statistical data analysis by taking multiple actual situations using the open-source software R version 4.0 and Python 3.0+. A detailed study of the statistical models is provided with examples related to health, agriculture, insurance, and other sectors. Each chapter will help you to increase your knowledge starting from basic statistics to advanced statistics. Key features: Discusses the importance of probability in the field of applied statistics and its importance in day-to-day life; Discusses methods for graphical representations and summary statistics with the help of numerous examples related to actual situations; Considers which distribution theories should be applied in different situations; Shows how to handle real-life problems related to probability; Introduces different ways of data handling using various software; Topics include random variables, statistical properties and theorems, discrete probability models, Weibull distributions, sample generation, Pareto and Burr distributions, data analysis through the freely available statistical package Python, and more. Written clearly for both students and researchers, this volume will be a valuable resource on distribution theories and their applications."--
Author : J.J. Duistermaat
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 48,67 MB
Release : 2010-08-09
Category : Mathematics
ISBN : 0817646752
This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Author : Abdellah El Kinani
Publisher : World Scientific
Page : 219 pages
File Size : 15,94 MB
Release : 2010
Category : Mathematics
ISBN : 9814304921
The general frame for the resolution of PDEs is the theory of kernels ù the first elements of which are sufficient to show the practicality of distribution theory in applications. --
Author : B. N. Pandey
Publisher : Narosa Publishing House
Page : 232 pages
File Size : 16,32 MB
Release : 2007
Category : Mathematics
ISBN :
Statistical Techniques in Life-Testing, Reliability, Sampling Theory and Quality Control covers recent research in the unified branches of theoretical and applied Statistics on common platform. These generally involve the concept of probability theory, prior information (Bayes and Minimax both), distribution theory, order statistics censoring, Truncation, loss and risk function, conditional distribution (sufficiency and complete sufficiency), sampling techniques using non-response techniques and Post- Stratification etc. Log-normal models in survival data, Bernoulli's trials, regression, ration under non necessarily model, CUSUM techniques in control charts, and reliability models with wide applications in other disciplines such as biology, mining and coal, industries, agriculture population, science and technology, medical sciences, research organizations, engineering, operation research, cancer institute, defense organizations, etc. are also discussed.
Author : A.H. Zemanian
Publisher : Courier Corporation
Page : 404 pages
File Size : 47,37 MB
Release : 2011-11-30
Category : Mathematics
ISBN : 0486151948
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
