Probability And Statistical Models

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Probability and Statistical Models

Arjun K. Gupta,Wei-Bin Zeng,Yanhong Wu
Probability and Statistical Models Book PDF

Author : Arjun K. Gupta,Wei-Bin Zeng,Yanhong Wu
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 45,8 Mb
Release : 2010-08-26
Category : Mathematics
ISBN : 9780817649876

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Probability and Statistical Models by Arjun K. Gupta,Wei-Bin Zeng,Yanhong Wu Pdf

With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. In particular, emphasis is placed on laying the foundation for solving problems in reliability, insurance, finance, and credit risk. The material has been carefully selected to cover the basic concepts and techniques on each topic, making this an ideal introductory gateway to more advanced learning. With exercises and solutions to selected problems accompanying each chapter, this textbook is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics.

Models for Probability and Statistical Inference

James H. Stapleton
Models for Probability and Statistical Inference Book PDF

Author : James H. Stapleton
Publisher : John Wiley & Sons
Page : 466 pages
File Size : 44,7 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9780470183403

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Models for Probability and Statistical Inference by James H. Stapleton Pdf

This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readers Models for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping. Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses modes of convergence of sequences of random variables, with special attention to convergence in distribution. The second half of the book addresses statistical inference, beginning with a discussion on point estimation and followed by coverage of consistency and confidence intervals. Further areas of exploration include: distributions defined in terms of the multivariate normal, chi-square, t, and F (central and non-central); the one- and two-sample Wilcoxon test, together with methods of estimation based on both; linear models with a linear space-projection approach; and logistic regression. Each section contains a set of problems ranging in difficulty from simple to more complex, and selected answers as well as proofs to almost all statements are provided. An abundant amount of figures in addition to helpful simulations and graphs produced by the statistical package S-Plus(r) are included to help build the intuition of readers.

Probability and Statistical Models with Applications

CH. A. Charalambides,M.V. Koutras,N. Balakrishnan
Probability and Statistical Models with Applications Book PDF

Author : CH. A. Charalambides,M.V. Koutras,N. Balakrishnan
Publisher : CRC Press
Page : 665 pages
File Size : 46,8 Mb
Release : 2000-09-21
Category : Mathematics
ISBN : 9781420036084

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Probability and Statistical Models with Applications by CH. A. Charalambides,M.V. Koutras,N. Balakrishnan Pdf

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, Probabili

Probability and Statistical Inference

Miltiadis C. Mavrakakis,Jeremy Penzer
Probability and Statistical Inference Book PDF

Author : Miltiadis C. Mavrakakis,Jeremy Penzer
Publisher : CRC Press
Page : 444 pages
File Size : 41,8 Mb
Release : 2021-03-28
Category : Mathematics
ISBN : 9781315362045

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Probability and Statistical Inference by Miltiadis C. Mavrakakis,Jeremy Penzer Pdf

Probability and Statistical Inference: From Basic Principles to Advanced Models covers aspects of probability, distribution theory, and inference that are fundamental to a proper understanding of data analysis and statistical modelling. It presents these topics in an accessible manner without sacrificing mathematical rigour, bridging the gap between the many excellent introductory books and the more advanced, graduate-level texts. The book introduces and explores techniques that are relevant to modern practitioners, while being respectful to the history of statistical inference. It seeks to provide a thorough grounding in both the theory and application of statistics, with even the more abstract parts placed in the context of a practical setting. Features: •Complete introduction to mathematical probability, random variables, and distribution theory. •Concise but broad account of statistical modelling, covering topics such as generalised linear models, survival analysis, time series, and random processes. •Extensive discussion of the key concepts in classical statistics (point estimation, interval estimation, hypothesis testing) and the main techniques in likelihood-based inference. •Detailed introduction to Bayesian statistics and associated topics. •Practical illustration of some of the main computational methods used in modern statistical inference (simulation, boostrap, MCMC). This book is for students who have already completed a first course in probability and statistics, and now wish to deepen and broaden their understanding of the subject. It can serve as a foundation for advanced undergraduate or postgraduate courses. Our aim is to challenge and excite the more mathematically able students, while providing explanations of statistical concepts that are more detailed and approachable than those in advanced texts. This book is also useful for data scientists, researchers, and other applied practitioners who want to understand the theory behind the statistical methods used in their fields.

Geometric Modeling in Probability and Statistics

Ovidiu Calin,Constantin Udrişte
Geometric Modeling in Probability and Statistics Book PDF

Author : Ovidiu Calin,Constantin Udrişte
Publisher : Springer
Page : 389 pages
File Size : 47,6 Mb
Release : 2014-07-17
Category : Mathematics
ISBN : 9783319077796

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Geometric Modeling in Probability and Statistics by Ovidiu Calin,Constantin Udrişte Pdf

This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable reference for researchers and graduate students in one of the aforementioned fields. This textbook is a unified presentation of differential geometry and probability theory, and constitutes a text for a course directed at graduate or advanced undergraduate students interested in applications of differential geometry in probability and statistics. The book contains over 100 proposed exercises meant to help students deepen their understanding, and it is accompanied by software that is able to provide numerical computations of several information geometric objects. The reader will understand a flourishing field of mathematics in which very few books have been written so far.

Nonlinear Statistical Models

A. Ronald Gallant
Nonlinear Statistical Models Book PDF

Author : A. Ronald Gallant
Publisher : John Wiley & Sons
Page : 632 pages
File Size : 40,9 Mb
Release : 1987-02-04
Category : Mathematics
ISBN : UOM:39015017305916

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Nonlinear Statistical Models by A. Ronald Gallant Pdf

Univariate nonlinear regression; Univariate nonlinear regression: special situations; A unified asymptotic theory of nonlinear models with regression structure; Univariate nonlinear regression: asymptotic theory; Multivariate nonlinear regression; Nonlinear simultaneus equations models; A unified asymptotic theory for dynamic nonlinear models.

Introduction to Probability

Narayanaswamy Balakrishnan,Markos V. Koutras,Konstadinos G. Politis
Introduction to Probability Book PDF

Author : Narayanaswamy Balakrishnan,Markos V. Koutras,Konstadinos G. Politis
Publisher : John Wiley & Sons
Page : 548 pages
File Size : 51,9 Mb
Release : 2021-11-24
Category : Mathematics
ISBN : 9781118548554

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Introduction to Probability by Narayanaswamy Balakrishnan,Markos V. Koutras,Konstadinos G. Politis Pdf

INTRODUCTION TO PROBABILITY Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite. This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory. A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text: Includes classroom-tested problems and solutions to probability exercises Highlights real-world exercises designed to make clear the concepts presented Uses Mathematica software to illustrate the text’s computer exercises Features applications representing worldwide situations and processes Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Uncertainty

William Briggs
Uncertainty Book PDF

Author : William Briggs
Publisher : Springer
Page : 258 pages
File Size : 46,6 Mb
Release : 2016-07-15
Category : Mathematics
ISBN : 9783319397566

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Uncertainty by William Briggs Pdf

This book presents a philosophical approach to probability and probabilistic thinking, considering the underpinnings of probabilistic reasoning and modeling, which effectively underlie everything in data science. The ultimate goal is to call into question many standard tenets and lay the philosophical and probabilistic groundwork and infrastructure for statistical modeling. It is the first book devoted to the philosophy of data aimed at working scientists and calls for a new consideration in the practice of probability and statistics to eliminate what has been referred to as the "Cult of Statistical Significance." The book explains the philosophy of these ideas and not the mathematics, though there are a handful of mathematical examples. The topics are logically laid out, starting with basic philosophy as related to probability, statistics, and science, and stepping through the key probabilistic ideas and concepts, and ending with statistical models. Its jargon-free approach asserts that standard methods, such as out-of-the-box regression, cannot help in discovering cause. This new way of looking at uncertainty ties together disparate fields — probability, physics, biology, the “soft” sciences, computer science — because each aims at discovering cause (of effects). It broadens the understanding beyond frequentist and Bayesian methods to propose a Third Way of modeling.

Linear Statistical Models

James H. Stapleton
Linear Statistical Models Book PDF

Author : James H. Stapleton
Publisher : John Wiley & Sons
Page : 517 pages
File Size : 41,5 Mb
Release : 2009-08-03
Category : Mathematics
ISBN : 9780470231463

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Linear Statistical Models by James H. Stapleton Pdf

Praise for the First Edition "This impressive and eminently readable text . . . [is] a welcome addition to the statistical literature." —The Indian Journal of Statistics Revised to reflect the current developments on the topic, Linear Statistical Models, Second Edition provides an up-to-date approach to various statistical model concepts. The book includes clear discussions that illustrate key concepts in an accessible and interesting format while incorporating the most modern software applications. This Second Edition follows an introduction-theorem-proof-examples format that allows for easier comprehension of how to use the methods and recognize the associated assumptions and limits. In addition to discussions on the methods of random vectors, multiple regression techniques, simultaneous confidence intervals, and analysis of frequency data, new topics such as mixed models and curve fitting of models have been added to thoroughly update and modernize the book. Additional topical coverage includes: An introduction to R and S-Plus® with many examples Multiple comparison procedures Estimation of quantiles for regression models An emphasis on vector spaces and the corresponding geometry Extensive graphical displays accompany the book's updated descriptions and examples, which can be simulated using R, S-Plus®, and SAS® code. Problems at the end of each chapter allow readers to test their understanding of the presented concepts, and additional data sets are available via the book's FTP site. Linear Statistical Models, Second Edition is an excellent book for courses on linear models at the upper-undergraduate and graduate levels. It also serves as a comprehensive reference for statisticians, engineers, and scientists who apply multiple regression or analysis of variance in their everyday work.

Statistical Modeling and Computation

Dirk P. Kroese,Joshua C.C. Chan
Statistical Modeling and Computation Book PDF

Author : Dirk P. Kroese,Joshua C.C. Chan
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 50,8 Mb
Release : 2013-11-18
Category : Computers
ISBN : 9781461487753

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Statistical Modeling and Computation by Dirk P. Kroese,Joshua C.C. Chan Pdf

This textbook on statistical modeling and statistical inference will assist advanced undergraduate and graduate students. Statistical Modeling and Computation provides a unique introduction to modern Statistics from both classical and Bayesian perspectives. It also offers an integrated treatment of Mathematical Statistics and modern statistical computation, emphasizing statistical modeling, computational techniques, and applications. Each of the three parts will cover topics essential to university courses. Part I covers the fundamentals of probability theory. In Part II, the authors introduce a wide variety of classical models that include, among others, linear regression and ANOVA models. In Part III, the authors address the statistical analysis and computation of various advanced models, such as generalized linear, state-space and Gaussian models. Particular attention is paid to fast Monte Carlo techniques for Bayesian inference on these models. Throughout the book the authors include a large number of illustrative examples and solved problems. The book also features a section with solutions, an appendix that serves as a MATLAB primer, and a mathematical supplement.​

Parametric Statistical Models and Likelihood

Ole E Barndorff-Nielsen
Parametric Statistical Models and Likelihood Book PDF

Author : Ole E Barndorff-Nielsen
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 55,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239345

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Parametric Statistical Models and Likelihood by Ole E Barndorff-Nielsen Pdf

This book is a slightly revised and expanded version of a set I I I of notes used for a lecture series given at the Ecole dlEte de I Probabilites at st. Flour in August 1986. In view of the statistical nature of the material discussed herein it was agreed to publish the material as a separate volume in the statistics series rather than, as is the tradition, in a joint volume in the Lecture Notes in Mathematics Series. It is a genuine pleasure to have this opportunity to thank I I I the organizers of Les Ecoles dlEte, and in particular Professor P. -L. Hennequin, for the excellent arrangements of these Summer Schools which form a very significant forum for the exchange of scientific ideas relating to probability. The efficient, careful and patient preparation of the typescript by Oddbj~rg Wethelund is also gratefully acknowledged. Aarhus, June 1988 O. E. Barndorff-Nielsen Parametric statistical Models and Likelihood O. E. Barndorff-Nielsen o. Introduction 0. 1. Outline of contents 1 0. 2. A few preliminaries 2 1. Likelihood and auxiliary statistics 1. 1. Likelihood 4 1. 2. Moments and cumulants of log likelihood derivatives 10 1. 3. Parametrization invariance 13 1. 4. Marginal and conditional likelihood 15 * 1. 5. Combinants, auxiliaries, and the p -model 19 1. 6. Orthogonal parameters 27 1. 7. Pseudo likelihood, profile likelihood and modified 30 profile likelihood 1. 8. Ancillarity and conditionality 33 41 1. 9. Partial sufficiency and partial ancillarity 1. 10.

Philosophy of Probability and Statistical Modelling

Mauricio Suárez
Philosophy of Probability and Statistical Modelling Book PDF

Author : Mauricio Suárez
Publisher : Cambridge University Press
Page : 128 pages
File Size : 42,8 Mb
Release : 2021-01-21
Category : Philosophy
ISBN : 9781108983846

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Philosophy of Probability and Statistical Modelling by Mauricio Suárez Pdf

This Element has two main aims. The first one (sections 1-7) is an historically informed review of the philosophy of probability. It describes recent historiography, lays out the distinction between subjective and objective notions, and concludes by applying the historical lessons to the main interpretations of probability. The second aim (sections 8-13) focuses entirely on objective probability, and advances a number of novel theses regarding its role in scientific practice. A distinction is drawn between traditional attempts to interpret chance, and a novel methodological study of its application. A radical form of pluralism is then introduced, advocating a tripartite distinction between propensities, probabilities and frequencies. Finally, a distinction is drawn between two different applications of chance in statistical modelling which, it is argued, vindicates the overall methodological approach. The ensuing conception of objective probability in practice is the 'complex nexus of chance'.

Statistical Models

A. C. Davison
Statistical Models Book PDF

Author : A. C. Davison
Publisher : Cambridge University Press
Page : 1026 pages
File Size : 47,5 Mb
Release : 2003-08-04
Category : Mathematics
ISBN : 9781139437417

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Statistical Models by A. C. Davison Pdf

Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Probability and Statistics with R

Maria Dolores Ugarte,Ana F. Militino,Alan T. Arnholt
Probability and Statistics with R Book PDF

Author : Maria Dolores Ugarte,Ana F. Militino,Alan T. Arnholt
Publisher : CRC Press
Page : 710 pages
File Size : 40,7 Mb
Release : 2008-04-11
Category : Mathematics
ISBN : 9781584888925

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Probability and Statistics with R by Maria Dolores Ugarte,Ana F. Militino,Alan T. Arnholt Pdf

Designed for an intermediate undergraduate course, Probability and Statistics with R shows students how to solve various statistical problems using both parametric and nonparametric techniques via the open source software R. It provides numerous real-world examples, carefully explained proofs, end-of-chapter problems, and illuminating graphs

Probability, Statistics and Modelling in Public Health

M.S. Nikulin,Daniel Commenges,Catherine Huber-Carol
Probability Statistics and Modelling in Public Health Book PDF

Author : M.S. Nikulin,Daniel Commenges,Catherine Huber-Carol
Publisher : Springer
Page : 480 pages
File Size : 45,7 Mb
Release : 2005-10-11
Category : Medical
ISBN : 0387260226

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Probability, Statistics and Modelling in Public Health by M.S. Nikulin,Daniel Commenges,Catherine Huber-Carol Pdf

Probability, Statistics and Modelling in Public Health consists of refereed contributions by expert biostatisticians that discuss various probabilistic and statistical models used in public health. Many of them are based on the work of Marvin Zelen of the Harvard School of Public Health. Topics discussed include models based on Markov and semi-Markov processes, multi-state models, models and methods in lifetime data analysis, accelerated failure models, design and analysis of clinical trials, Bayesian methods, pharmaceutical and environmental statistics, degradation models, epidemiological methods, screening programs, early detection of diseases, and measurement and analysis of quality of life.