Statistical Consequences of Fat Tails

Statistical Consequences of Fat Tails

This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.

Author: Nassim Nicholas Taleb

Publisher:

ISBN: 1544508050

Category:

Page:

View: 929

The book investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress." Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the "laws of the medium numbers"-which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on "naïve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.
Categories:

Control Performance Assessment Theoretical Analyses and Industrial Practice

Control Performance Assessment  Theoretical Analyses and Industrial Practice

J. 16(7), 1998–2003 (2016) Taleb, N.N.: Real-world Statistical Consequences of Fat Tails: Papers and Commentary. STEM Academic Press, Technical Incerto Collection (2018) Verboven, S., Hubert, M.: LIBRA: a Matlab library for robust ...

Author: Paweł D. Domański

Publisher: Springer Nature

ISBN: 9783030235932

Category: Technology & Engineering

Page: 367

View: 737

This book presents a comprehensive review of currently available Control Performance Assessment methods. It covers a broad range of classical and modern methods, with a main focus on assessment practice, and is intended to help practitioners learn and properly perform control assessment in the industrial reality. Further, it offers an educational guide for control engineers, who are currently in high demand in the industry. The book consists of three main parts. Firstly, a comprehensive review of available approaches is presented and discussed. The classical canon methods are extended with a discussion of nonlinear and complex alternative measures using non-Gaussian statistics, persistence and fractional calculations. Secondly, the methods’ applicability aspects are visualized with the aid of computer simulations, covering the most popular control philosophies used in the process industry. Lastly, a critical review of the methods discussed, on the basis of real-world industrial examples, rounds out the coverage.
Categories: Technology & Engineering

Unifying Themes in Complex Systems IX

Unifying Themes in Complex Systems IX

The Statistical Consequences of Fat Tails, vol. 1 (2018). www.fooledbyrandomness.com Einmahl, J., Einmahl, J., de Haan, L.: Limits to Human Life Span Through Extreme Value Theory. Center Discussion Paper Series No. 2017-051.

Author: Alfredo J. Morales

Publisher: Springer

ISBN: 9783319966618

Category: Science

Page: 506

View: 269

Unifying Themes in Complex Systems is a well-established series of carefully edited conference proceedings that serve to document and archive the progress made regarding cross-fertilization in this field. The International Conference on Complex Systems (ICCS) creates a unique atmosphere for scientists from all fields, engineers, physicians, executives, and a host of other professionals, allowing them to explore common themes and applications of complex systems science. With this new volume, Unifying Themes in Complex Systems continues to establish common ground between the wide-ranging domains of complex systems science.
Categories: Science

Nonlinear Dynamics and Control

Nonlinear Dynamics and Control

Taleb, N.N.: Real-World Statistical Consequences of Fat Tails: Papers and Commentary, Technical Incerto Collection. STEM Academic, Rockville (2018) Impact of the Controller Algorithm on the Effect of Motor 156 P. D. Doma ́nski and M.

Author: Walter Lacarbonara

Publisher: Springer Nature

ISBN: 9783030347475

Category: Science

Page: 349

View: 930

This second of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to Nonlinear Dynamics and Control. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume II include influence of nonlinearities on vibration control systems; passive, semi-active, active control of structures and systems; synchronization; robotics and human-machine interaction; network dynamics control (multi-agent systems, leader-follower dynamics, swarm dynamics, biological networks dynamics); and fractional-order control.
Categories: Science

Globalization Gating and Risk Finance

Globalization  Gating  and Risk Finance

2.2.3 Outliers, Extreme Statistics, and Fat Tails Outliers are events in a data set that do not conform to their predicted occurrences. ... 2.2.4 Extreme Risks Extreme risks are characterized by rare events or by extreme consequences.

Author: Unurjargal Nyambuu

Publisher: John Wiley & Sons

ISBN: 9781119252658

Category: Business & Economics

Page: 496

View: 365

An in-depth guide to global and risk finance based on financial models and data-based issues that confront global financial managers. Globalization, Gating, and Risk Finance offers perspectives on global risk finance in a world with economies in transition. Developed from lectures and research projects investigating the consequences of globalization and strategic approaches to fundamental economics and finance, it provides an approach based on financial models and data; it includes many case-study problems. The book departs from the traditional macroeconomic and financial approaches to global and strategic risk finance, where economic power and geopolitical issues are intermingled to create complex and forward-looking financial systems. Chapter coverage includes: Globalization: Economies in Collision; Data, Measurements, and Global Finance; Global Finance: Utility, Financial Consumption, and Asset Pricing; Macroeconomics, Foreign Exchange, and Global Finance; Foreign Exchange Models and Prices; Asia: Financial Environment and Risks; Financial Currency Pricing, Swaps, Derivatives, and Complete Markets; Credit Risk and International Debt; Globalization and Trade: A Changing World; and Compliance and Financial Regulation. Provides a framework for global financial and inclusive models, some of which are not commonly covered in other books. Considers risk management, utility, and utility-based multi-agent financial theories. Presents a theoretical framework to assist with a variety of problems ranging from derivatives and FX pricing to bond default to trade and strategic regulation. Provides detailed explanations and mathematical proofs to aid the readers’ understanding. Globalization, Gating, and Risk Finance is appropriate as a text for graduate students of global finance, general finance, financial engineering, and international economics, and for practitioners.
Categories: Business & Economics

Statistical Methods in Healthcare

Statistical Methods in Healthcare

A second dimension relates to 'unforecastable events', defined by probability distributions with fat tails. In the first layer, exceptions occur without significant consequences since they are predictable. The traditional random walk, ...

Author: Frederick W. Faltin

Publisher: John Wiley & Sons

ISBN: 9781119942047

Category: Medical

Page: 520

View: 701

In recent years the number of innovative medicinal products and devices submitted and approved by regulatory bodies has declined dramatically. The medical product development process is no longer able to keep pace with increasing technologies, science and innovations and the goal is to develop new scientific and technical tools and to make product development processes more efficient and effective. Statistical Methods in Healthcare focuses on the application of statistical methodologies to evaluate promising alternatives and to optimize the performance and demonstrate the effectiveness of those that warrant pursuit is critical to success. Statistical methods used in planning, delivering and monitoring health care, as well as selected statistical aspects of the development and/or production of pharmaceuticals and medical devices are also addressed. With a focus on finding solutions to these challenges, this book: Provides a comprehensive, in-depth treatment of statistical methods in healthcare, along with a reference source for practitioners and specialists in health care and drug development. Offers a broad coverage of standards and established methods through leading edge techniques. Uses an integrated, case-study based approach, with focus on applications. Looks at the use of analytical and monitoring schemes to evaluate therapeutic performance. Features the application of modern quality management systems to clinical practice, and to pharmaceutical development and production processes. Addresses the use of modern Statistical methods such as Adaptive Design, Seamless Design, Data Mining, Bayesian networks and Bootstrapping that can be applied to support the challenging new vision. Practitioners in healthcare-related professions, ranging from clinical trials to care delivery to medical device design, as well as statistical researchers in the field, will benefit from this book.
Categories: Medical

Analysis of Catastrophes and Their Public Health Consequences

Analysis of Catastrophes and Their Public Health Consequences

The probability density function of a fat-tailed distribution, for large x ∈ X, goes to zero as x−α: fat-tailed ... The statistic of importance for these determinations is the moment generating function of the distribution, ...

Author: Paolo F. Ricci

Publisher: Springer Nature

ISBN: 9783030480660

Category: Medical

Page: 187

View: 481

Public health policy prospectively and retrospectively addresses the consequences of events ranging from the commonplace to the catastrophic. Informing policymakers and stakeholders by enhancing their understanding of complex causation to justify remedial or precautionary actions is a critical science-policy task. In this book, the key aspects of catastrophes (regardless of their nature) and routine events are identified through a common framework for their analyses, and the analyses of the consequences associated with the potential occurrence of these events also are discussed. The book is not about disaster planning; instead, it is focused on analysis and causation in the context of informing – rather than formulating – public health policy. The author aggregates and fuses scientific information and knowledge in public health policy-science using alternative but complementary methods. The book first focuses on the analysis of catastrophes and commonplace events; the focus then shifts to causal models of multifactorial diseases, particularly at low doses or dose-rates, associated with these events. Topics explored among the chapters include: Policy and Legal Aspects of Precautionary Choices Catastrophes, Disasters, and Calamities: Concepts for Their Assessment Uncertainty: Probabilistic and Statistical Aspects Aggregating Judgments to Inform Precautionary Decision-making The aim of the book is to show that the analyses of events are fundamentally similar, regardless of whether the concern is a global catastrophe or commonplace. Analysis of Catastrophes and Their Public Health Consequences is a text that should engage students, instructors, and researchers in public health, science policy, and preparedness research, as well as serve as a useful resource for policy analysts, practitioners, and risk managers.
Categories: Medical

Advances in Solid State Physics

Advances in Solid State Physics

Fat Tail Statistics and Beyond Joachim Peinke ?, Malte Siefert ?, Stephan Barth ?, Christoph Renner ?, Falk Riess ? ... On the other side , such statistics have very important consequences for applications , as it is the case for risk ...

Author: Bernhard Kramer

Publisher: Springer Science & Business Media

ISBN: 3540211489

Category: Science

Page: 566

View: 535

This Volume 44 of Advances in Solid State Physics contains the written versions of most of the invited lectures of the Spring Meeting of the Condensed Matter Physics section of the Deutsche Physikalische Gesellschaft held from March 8 to 12, 2004 in Regensburg, Germany. Many of the topical talks given at the numerous and very lively symposia are also included. They have covered extremely interesting and timely subjects. Thus the book truly reflects the status of the field of solid state physics in 2004, and indicates its importance, not only in Germany but also internationally.
Categories: Science

Fatigue Durability and Fracture Mechanics

Fatigue  Durability  and Fracture Mechanics

According to Taleb [32], a simplistic view of the statistics of Gaussian normal curve does not reflect the actual risks; and there are risks with 'fat tails' that would normally be expected to be rare or extreme event, but actually ...

Author: S. Seetharamu

Publisher: Springer Nature

ISBN: 9789811547799

Category: Coatings

Page: 645

View: 529

This book presents selected papers presented during Fatigue Durability India 2019. The contents of this volume discuss advances in the field of fatigue, durability, and fracture, and cover mechanical failure and its applications. The chapters cover a wide spectrum of topics, including design, engineering, testing and computational evaluation of the components or systems for fatigue, durability, and fracture mechanics. The contents of this book will appeal not only to academic researchers, but also to design engineers, failure analysts, maintenance engineers, certification personnel, and R&D professionals involved in a wide variety of industries.
Categories: Coatings

Handbook on the Economics of Climate Change

Handbook on the Economics of Climate Change

... consequences of fat-tailed structural uncertainty (along with unsureness about hightemperature damages) can outweigh the effects of discounting in climate-change policy analysis (Weitzman, 2009). He suggested adopting a statistical ...

Author: Graciela Chichilnisky

Publisher: Edward Elgar Publishing

ISBN: 9780857939067

Category: Science

Page: 464

View: 925

This timely Handbook recognises the emergence of climate change as the defining topic of our time. With public climate discourse growing more urgent every year, this Handbook brings together international experts from different economic disciplines to answer critical climate policy questions.
Categories: Science

A Practical Guide to Heavy Tails

A Practical Guide to Heavy Tails

Statistical Techniques and Applications Robert Adler, Raya Feldman, Murad Taqqu ... In section 5 , we examine the behavior of the Hill estimator for different types of fat - tailed distributions and as a function of the ...

Author: Robert Adler

Publisher: Springer Science & Business Media

ISBN: 0817639519

Category: Mathematics

Page: 534

View: 890

Twenty-four contributions, intended for a wide audience from various disciplines, cover a variety of applications of heavy-tailed modeling involving telecommunications, the Web, insurance, and finance. Along with discussion of specific applications are several papers devoted to time series analysis, regression, classical signal/noise detection problems, and the general structure of stable processes, viewed from a modeling standpoint. Emphasis is placed on developments in handling the numerical problems associated with stable distribution (a main technical difficulty until recently). No index. Annotation copyrighted by Book News, Inc., Portland, OR
Categories: Mathematics

Complex Materials in Physics and Biology

Complex Materials in Physics and Biology

The breakdown of Gaussian statistics appears as a fat tail in this distribution. This fat tail indicates ... The physical consequences of this fat tail and corresponding crossover in length scale are discussed in the next lecture. 3.

Author: F. Mallamace

Publisher: IOS Press

ISBN: 9781614990710

Category: Science

Page: 450

View: 786

The surprising connections which have developed between physics and various fields as diverse as biology and economics now constitute the fascinating research area known as complex materials and systems. The study of complex materials and processes is rapidly expanding, and many important experimental and theoretical discoveries have been made in recent years. Statistical physics is key to exploring this new and expanding field, enabling an understanding of real-world phenomena compromised of complex materials or exhibiting complex processes. This book includes lectures presented at the CLXXVI International School of Physics “Enrico Fermi”, held in Varenna, Italy, in July 2010. The school focused on recent advances and developing perspectives in the study of complex materials and processes, as related to physics and biology. The book provides both an introduction and a complete presentation of recent theoretical and experimental developments for each topic. Topics addressed include: scaling and universality, supra-molecular systems and solutions, polymer systems, static and dynamics of liquid water, arrested dynamics and jamming, dynamics of out of equilibrium systems, physics of confined liquids, granular matter, physics of biological and medical systems, networks in physical and social sciences, turbulence in physics, biology and economics and finally, switching phenomena in biology and economics. The book provides reviews of these cutting edge topics by leading authorities and will be a reference work useful to both advanced research professionals and beginning graduate students.
Categories: Science

Behavioral Finance for Private Banking

Behavioral Finance for Private Banking

A statistical consequence of prices being unpredictable is that returns are (log)‐normally distributed—which is the content of ... For example, they have fat tails (i.e., too many very bad returns)—which Taleb (2007) called black swans.

Author: Kremena K. Bachmann

Publisher: John Wiley & Sons

ISBN: 9781119453710

Category: Business & Economics

Page: 256

View: 318

An essential framework for wealth management using behavioral finance Behavioral Finance for Private Banking provides a complete framework for wealth management tailored to the unique needs of each client. Merging behavioral finance with private banking, this framework helps you gain a greater understanding of your client’s wants, needs, and perspectives to streamline the decision making process. Beginning with the theoretical foundations of investment decision making and behavioral biases, the discussion delves into cultural differences in global business and asset allocation over the life cycle of the investment to help you construct a wealth management strategy catered to each individual’s needs. This new second edition has been updated to include coverage of fintech and neurofinance, an extension of behavioral finance that is beginning to gain traction in the private banking space. Working closely with clients entails deep interpersonal give and take. To be successful, private banking professionals must be as well-versed in behavioral psychology as they are in finance; this intersection is the heart of behavioral finance, and this book provides essential knowledge that can help you better serve your clients’ needs. Understand the internal dialogue at work when investment decisions are made Overcome the most common behavioral biases—and watch for your own Learn how fintech and neurofinance impact all aspects of private banking Set up a structured wealth management process that places the client’s needs front and center Private banking clients demand more than just financial expertise. They want an advisor who truly understands their needs, and can develop and execute the kind of strategy that will help them achieve their goals. Behavioral Finance for Private Banking provides a complete framework alongside insightful discussion to help you become the solution your clients seek.
Categories: Business & Economics

Strategic Risk Management

Strategic Risk Management

This becomes particularly critical in fat-tailed domains where conventional statistical measures cease to have any ... events in the tails that often represent the real strategic risks with large potential upsides and downsides.

Author: Torben Juul Andersen

Publisher: Routledge

ISBN: 9780429851568

Category: Business & Economics

Page: 112

View: 776

Organizations face challenges in adapting their current business and operational activities to dynamic contexts. Successful companies share a common characteristic of dealing with the emergent risks and threats in responses that generate viable solutions. Strategic risk management (SRM) is a multidisciplinary and rather fractured field of study, which creates significant challenges for research. This short-form book provides an expert overview of the topic, providing insight into the theory and practice. Essential reading for strategic management researchers, the authors frame the fundamental principles, emerging challenges and responses for the future, which will also provide valuable insights for adjacent business disciplines and beyond.
Categories: Business & Economics

The SAGE Dictionary of Statistics Methodology

The SAGE Dictionary of Statistics   Methodology

The left (low X value) end of the distribution is more “fat tailed. ... This might involve, for example, taking the presence of an effect to argue for the presence of a cause, which is then claimed to bring about the effect.

Author: W. Paul Vogt

Publisher: SAGE Publications

ISBN: 9781483381787

Category: Reference

Page: 520

View: 787

Written in a clear, readable style with a wide range of explanations and examples, this must-have dictionary reflects recent changes in the fields of statistics and methodology. Packed with new definitions, terms, and graphics, this invaluable resource is an ideal reference for researchers and professionals in the field and provides everything students need to read and understand a research report, including elementary terms, concepts, methodology, and design definitions, as well as concepts from qualitative research methods and terms from theory and philosophy. Looking for an eBook versions of this title which include features such as search functionality, bookmarks, note-taking tools and more? Upon publication, this title will be offered on Amazon Kindle, Vital Source, and on additional eBook platforms. Check your preferred platform for current availability.
Categories: Reference

Natural and Man Made Catastrophes

Natural and Man Made Catastrophes

An infinity of uncertainty gives rise to a fat-tail distribution of a statistical event (Schuster 1984). climate In ... Looking east, we find a treasure trove of thinkers and philosophies that preached the concepts and consequences of ...

Author: S. Niggol Seo

Publisher: John Wiley & Sons

ISBN: 9781119416791

Category: Political Science

Page: 272

View: 227

A thorough explanation of the mathematical theories, philosophies, and economics of catastrophes with a view to how humanity should be prepared for events with catastrophic consequences This book presents a holistic view of natural and man-made catastrophes, from mathematical theories and philosophy through to economics and policy. It is both academic and applied in its approach, offering both empirical evidence and academic reflections to give a new perspective on an ever-developing topic, and providing many examples of public policy and catastrophe responses from around the world. Natural and Man-made Catastrophes: Theories, Economics, and Policy Designs begins by introducing readers to numerous natural and man-made catastrophes and how catastrophe theories have played a pivotal role in designing policies and responses to them. It discusses hurricanes, earthquakes, nuclear disaster, asteroid collision, Large Hadron Collider, artificial intelligence, uncontrollable robots, global warming, infectious diseases without antibodies, and bioterrorism. It clarifies key mathematical and scientific theories—such as catastrophe theory, chaos, singularity, fractal, tipping point, unbounded variance, fat-tail, and Feigenbaum constant—on catastrophes. The book goes on to examine ancient and contemporary philosophies that have played critical roles in humanity’s understanding of catastrophic outcomes. The book critically builds the economics of catastrophic events 1) by consolidating the catastrophe literature in natural sciences, scientific theories, and philosophy; 2) by constructing global empirical catastrophe data and analytical models using historical data on hurricanes and earthquakes; 3) and by critically reviewing policy experiences on the aforementioned catastrophic events. Lays the foundation for the economic analyses and policy-making on potential humanity/universe threatening catastrophes Includes many examples of public policy and behavioral responses to catastrophes from around the world Provides a wide-ranging commentary on crucial implications of the studies, models, and concepts of catastrophes Synthesizes the catastrophe literature in mathematical theories, philosophical traditions, economic analyses, policy studies, and contemporary concerns. Natural and Man-made Catastrophes: Theories, Economics, and Policy Designs is an important book for students, teachers, professionals, and policy makers who are involved in environmental research and disaster response.
Categories: Political Science

Managing Banking Risks

Managing Banking Risks

Catastrophic exposures of this kind occur in the 'long/fat tails' of a distribution of possible outcomes (see). In a bank, they are likely to emanate from operations where large monetary values or transaction volumes are concentrated ...

Author: Eddie Cade

Publisher: Routledge

ISBN: 9781135952143

Category: Business & Economics

Page: 250

View: 573

First Published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.
Categories: Business & Economics

Encyclopedia of Financial Models

Encyclopedia of Financial Models

Fully approximating a finite economic system with fat-tailed laws depends on an accurate statistical analysis of the ... We then explore the consequences of eliminating the assumption of independence and discuss different concepts of ...

Author: Frank J. Fabozzi

Publisher: John Wiley & Sons

ISBN: 9781118539903

Category: Business & Economics

Page: 736

View: 768

Volume 3 of the Encyclopedia of Financial Models The need for serious coverage of financial modeling has never been greater, especially with the size, diversity, and efficiency of modern capital markets. With this in mind, the Encyclopedia of Financial Models has been created to help a broad spectrum of individuals—ranging from finance professionals to academics and students—understand financial modeling and make use of the various models currently available. Incorporating timely research and in-depth analysis, Volume 3 of the Encyclopedia of Financial Models covers both established and cutting-edge models and discusses their real-world applications. Edited by Frank Fabozzi, this volume includes contributions from global financial experts as well as academics with extensive consulting experience in this field. Organized alphabetically by category, this reliable resource consists of forty-four informative entries and provides readers with a balanced understanding of today’s dynamic world of financial modeling. Volume 3 covers Mortgage-Backed Securities Analysis and Valuation, Operational Risk, Optimization Tools, Probability Theory, Risk Measures, Software for Financial Modeling, Stochastic Processes and Tools, Term Structure Modeling, Trading Cost Models, and Volatility Emphasizes both technical and implementation issues, providing researchers, educators, students, and practitioners with the necessary background to deal with issues related to financial modeling The 3-Volume Set contains coverage of the fundamentals and advances in financial modeling and provides the mathematical and statistical techniques needed to develop and test financial models Financial models have become increasingly commonplace, as well as complex. They are essential in a wide range of financial endeavors, and the Encyclopedia of Financial Models will help put them in perspective.
Categories: Business & Economics

Handbook Of Heavy tailed Distributions In Asset Management And Risk Management

Handbook Of Heavy tailed Distributions In Asset Management And Risk Management

Statistical methods derived from it can be employed in finance. The tail ... for portfolio risk measurement and stress-testing, as well as option pricing where the so-called smile effect can be explained by the presence of fat tails.

Author: Stoyan V Stoyanov

Publisher: World Scientific

ISBN: 9789813276215

Category: Business & Economics

Page: 600

View: 272

The study of heavy-tailed distributions allows researchers to represent phenomena that occasionally exhibit very large deviations from the mean. The dynamics underlying these phenomena is an interesting theoretical subject, but the study of their statistical properties is in itself a very useful endeavor from the point of view of managing assets and controlling risk. In this book, the authors are primarily concerned with the statistical properties of heavy-tailed distributions and with the processes that exhibit jumps. A detailed overview with a Matlab implementation of heavy-tailed models applied in asset management and risk managements is presented. The book is not intended as a theoretical treatise on probability or statistics, but as a tool to understand the main concepts regarding heavy-tailed random variables and processes as applied to real-world applications in finance. Accordingly, the authors review approaches and methodologies whose realization will be useful for developing new methods for forecasting of financial variables where extreme events are not treated as anomalies, but as intrinsic parts of the economic process.
Categories: Business & Economics

Process Improvement and CMMI for Systems and Software

Process Improvement and CMMI for Systems and Software

A second dimension relates to “unforecastable events,” defined by probability distributions with fat tails. In the first layer, exceptions occur without significant consequences because they are predictable. The traditional random walk, ...

Author: Ron S. Kenett

Publisher: CRC Press

ISBN: 9781000687385

Category: Business & Economics

Page: 435

View: 126

Process Improvement and CMMI for Systems and Software provides a workable approach for achieving cost-effective process improvements for systems and software. Focusing on planning, implementation, and management in system and software processes, it supplies a brief overview of basic strategic planning models and covers fundamental concepts and appr
Categories: Business & Economics