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Books in Statistics and probability

Exploring the fundamentals and advanced techniques of statistical analysis and probabilistic modeling, this selection supports data scientists, researchers, and decision-makers. It features cutting-edge methods, applications in industry, and case studies addressing uncertainty, risk assessment, and data-driven decision-making. These resources foster accurate interpretation, predictive analytics, and evidence-based insights essential for innovation in research, healthcare, finance, and policy development.

  • Survey Sampling Theory and Applications

    • 1st Edition
    • March 8, 2017
    • Raghunath Arnab
    • English
    Survey Sampling Theory and Applications offers a comprehensive overview of survey sampling, including the basics of sampling theory and practice, as well as research-based topics and examples of emerging trends. The text is useful for basic and advanced survey sampling courses. Many other books available for graduate students do not contain material on recent developments in the area of survey sampling. The book covers a wide spectrum of topics on the subject, including repetitive sampling over two occasions with varying probabilities, ranked set sampling, Fays method for balanced repeated replications, mirror-match bootstrap, and controlled sampling procedures. Many topics discussed here are not available in other text books. In each section, theories are illustrated with numerical examples. At the end of each chapter theoretical as well as numerical exercises are given which can help graduate students.

  • Introductory Statistics

    • 4th Edition
    • January 26, 2017
    • Sheldon M. Ross
    • English
    Introductory Statistics, Fourth Edition, reviews statistical concepts and techniques in a manner that will teach students not only how and when to utilize the statistical procedures developed, but also how to understand why these procedures should be used. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, an explanation of intuition, and the ideas behind the statistical methods. Concepts are motivated, illustrated, and explained in a way that attempts to increase one's intuition. To quote from the preface, it is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data. Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions, and examples. Applications and examples refer to real-world issues, such as gun control, stock price models, health issues, driving age limits, school admission ages, use of helmets, sports, scientific fraud, and many others. Examples relating to data mining techniques using the number of Google queries or Twitter tweets are also considered. For this fourth edition, new topical coverage includes sections on Pareto distribution and the 80-20 rule, Benford's law, added material on odds and joint distributions and correlation, logistic regression, A-B testing, and more modern (big data) examples and exercises.

  • Simulation of Stochastic Processes with Given Accuracy and Reliability

    • 1st Edition
    • November 22, 2016
    • Yuriy V. Kozachenko + 3 more
    • English
    Simulation has now become an integral part of research and development across many fields of study. Despite the large amounts of literature in the field of simulation and modeling, one recurring problem is the issue of accuracy and confidence level of constructed models. By outlining the new approaches and modern methods of simulation of stochastic processes, this book provides methods and tools in measuring accuracy and reliability in functional spaces.The authors explore analysis of the theory of Sub-Gaussian (including Gaussian one) and Square Gaussian random variables and processes and Cox processes. Methods of simulation of stochastic processes and fields with given accuracy and reliability in some Banach spaces are also considered.

  • Stochastic Models of Financial Mathematics

    • 1st Edition
    • October 12, 2016
    • Vigirdas Mackevicius
    • English
    This book presents a short introduction to continuous-time financial models. An overview of the basics of stochastic analysis precedes a focus on the Black–Scholes and interest rate models. Other topics covered include self-financing strategies, option pricing, exotic options and risk-neutral probabilities. Vasicek, Cox−Ingersoll−Ross, and Heath–Jarrow–Morton interest rate models are also explored.The author presents practitioners with a basic introduction, with more rigorous information provided for mathematicians. The reader is assumed to be familiar with the basics of probability theory. Some basic knowledge of stochastic integration and differential equations theory is preferable, although all preliminary information is given in the first part of the book. Some relatively simple theoretical exercises are also provided.

  • Ruin Probabilities

    Smoothness, Bounds, Supermartingale Approach
    • 1st Edition
    • October 10, 2016
    • Yuliya Mishura + 1 more
    • English
    Ruin Probabilities: Smoothness, Bounds, Supermartingale Approach deals with continuous-time risk models and covers several aspects of risk theory. The first of them is the smoothness of the survival probabilities. In particular, the book provides a detailed investigation of the continuity and differentiability of the infinite-horizon and finite-horizon survival probabilities for different risk models. Next, it gives some possible applications of the results concerning the smoothness of the survival probabilities. Additionally, the book introduces the supermartingale approach, which generalizes the martingale one introduced by Gerber, to get upper exponential bounds for the infinite-horizon ruin probabilities in some generalizations of the classical risk model with risky investments.

  • Analysis for Time-to-Event Data under Censoring and Truncation

    • 1st Edition
    • September 26, 2016
    • Hongsheng Dai + 1 more
    • English
    Survival Analysis for Bivariate Truncated Data provides readers with a comprehensive review on the existing works on survival analysis for truncated data, mainly focusing on the estimation of univariate and bivariate survival function. The most distinguishing feature of survival data is known as censoring, which occurs when the survival time can only be exactly observed within certain time intervals. A second feature is truncation, which is often deliberate and usually due to selection bias in the study design. Truncation presents itself in different ways. For example, left truncation, which is often due to a so-called late entry bias, occurs when individuals enter a study at a certain age and are followed from this delayed entry time. Right truncation arises when only individuals who experienced the event of interest before a certain time point can be observed. Analyzing truncated survival data without considering the potential selection bias may lead to seriously biased estimates of the time to event of interest and the impact of risk factors.

  • Fractional Calculus and Fractional Processes with Applications to Financial Economics

    Theory and Application
    • 1st Edition
    • September 22, 2016
    • Hasan Fallahgoul + 2 more
    • English
    Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.

  • Introduction to Robust Estimation and Hypothesis Testing

    • 4th Edition
    • September 2, 2016
    • Rand R. Wilcox
    • English
    Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions. New to this edition 35% revised content Covers many new and improved R functions New techniques that deal with a wide range of situations

  • Biostatistics and Computer-based Analysis of Health Data using Stata

    • 1st Edition
    • August 24, 2016
    • Christophe Lalanne + 1 more
    • English
    This volume of the Biostatistics and Health Sciences Set focuses on statistics applied to clinical research. The use of Stata for data management and statistical modeling is illustrated using various examples. Many aspects of data processing and statistical analysis of cross-sectional and experimental medical data are covered, including regression models commonly found in medical statistics. This practical book is primarily intended for health researchers with basic knowledge of statistical methodology. Assuming basic concepts, the authors focus on the practice of biostatistical methods essential to clinical research, epidemiology and analysis of biomedical data (including comparison of two groups, analysis of categorical data, ANOVA, linear and logistic regression, and survival analysis). The use of examples from clinical trials and epideomological studies provide the basis for a series of practical exercises, which provide instruction and familiarize the reader with essential Stata packages and commands.

  • Practical Business Statistics

    • 7th Edition
    • July 29, 2016
    • Andrew F. Siegel
    • English
    Practical Business Statistics, Seventh Edition, provides a conceptual, realistic, and matter-of-fact approach to managerial statistics that carefully maintains, but does not overemphasize mathematical correctness. The book provides deep understanding of how to learn from data and how to deal with uncertainty while promoting the use of practical computer applications. This valuable, accessible approach teaches present and future managers how to use and understand statistics without an overdose of technical detail, enabling them to better understand the concepts at hand and to interpret results. The text uses excellent examples with real world data relating to business sector functional areas such as finance, accounting, and marketing. Written in an engaging style, this timely revision is class-tested and designed to help students gain a solid understanding of fundamental statistical principles without bogging them down with excess mathematical details.

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