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Negative binomial distribution --- Tables

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There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach―that is, to incorporate prior knowledge when reasoning with incomplete information―in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data―and how to fix it.

Probabilities --- Mathematical statistics --- Law of large numbers --- Bernoulli, Jakob, 1654-1705 --- Binomial distribution. --- Law of large numbers. --- Influence (Literary, artistic, etc.) --- Philosophy --- History --- Philosophy. --- Bernoulli, Jakob, --- Influence. --- 1800-1999

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We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings… They are developed in eight chapters, with about a hundred of exercises.

Business mathematics. --- Distribution (Probability theory). --- Negative binomial distribution. --- Martingales (Mathematics) --- Finance --- Distribution (Probability theory) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Mathematical models --- Peafowl. --- Blue peafowl, Indian --- Common peafowl --- Indian blue peafowl --- Indian peafowl --- Pavo cristatus --- Peacocks --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Quantitative Finance. --- Stochastic processes --- Pavo --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology

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The analysis and modeling of time series is of the utmost importance in various fields of application. This Special Issue is a collection of articles on a wide range of topics, covering stochastic models for time series as well as methods for their analysis, univariate and multivariate time series, real-valued and discrete-valued time series, applications of time series methods to forecasting and statistical process control, and software implementations of methods and models for time series. The proposed approaches and concepts are thoroughly discussed and illustrated with several real-world data examples.

Humanities --- time series --- anomaly detection --- unsupervised learning --- kernel density estimation --- missing data --- multivariate time series --- nonstationary --- spectral matrix --- local field potential --- electric power --- forecasting accuracy --- machine learning --- extended binomial distribution --- INAR --- thinning operator --- time series of counts --- unemployment rate --- SARIMA --- SETAR --- Holt–Winters --- ETS --- neural network autoregression --- Romania --- integer-valued time series --- bivariate Poisson INGARCH model --- outliers --- robust estimation --- minimum density power divergence estimator --- CUSUM control chart --- INAR-type time series --- statistical process monitoring --- random survival rate --- zero-inflation --- cointegration --- subspace algorithms --- VARMA models --- seasonality --- finance --- volatility fluctuation --- Student’s t-process --- entropy based particle filter --- relative entropy --- count data --- time series analysis --- Julia programming language --- ordinal patterns --- long-range dependence --- multivariate data analysis --- limit theorems --- integer-valued moving average model --- counting series --- dispersion test --- Bell distribution --- count time series --- estimation --- overdispersion --- multivariate count data --- INGACRCH --- state-space model --- bank failures --- transactions --- periodic autoregression --- integer-valued threshold models --- parameter estimation --- models

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Sustainable industrial engineering addresses the sustainability issue from economic, environmental, and social points of view. Its application fields are the whole value chain and lifecycle of products/services, from the development to the end-of-life stages. This book aims to address many of the challenges faced by industrial organizations and supply chains to become more sustainable through reinventing their processes and practices, by continuously incorporating sustainability guidelines and practices in their decisions, such as circular economy, collaboration with suppliers and customers, using information technologies and systems, tracking their products’ life-cycle, using optimization methods to reduce resource use, and to apply new management paradigms to help mitigate many of the wastes that exist across organizations and supply chains. This book will be of interest to the fast-growing body of academics studying and researching sustainability, as well as to industry managers involved in sustainability management.

Technology: general issues --- information and communication technologies --- green supply chain --- update and sustainable --- sustainability --- green degree --- game model --- sustainable supplier selection --- DEMATEL --- ANP --- fuzzy VIKOR --- IVTFN --- hybrid information aggregation --- TBL theory --- energy intensity --- income --- education --- eco-efficiency --- circular economy --- equipment development task --- foreseeable rework --- hidden rework --- uncertainty --- complexity --- blockchain --- supply chain --- use cases --- applications --- quality level --- reliability demonstration test --- Bayesian approach --- conjugacy --- beta-binomial distribution --- sequential sampling --- one-shot devices --- finite population --- express delivery service --- last mile delivery --- pricing --- collaboration --- market share --- reverse supply chain --- collection strategy --- waste mobile phones --- evolutionary game theory --- evolution mechanism --- reward-penalty mechanism --- ammunition incineration --- down-cycling --- energetic material recycling --- industrial ecology --- life-cycle assessment --- cap-and-trade --- production --- carbon emissions reduction --- consumers’ environmental preferences --- newsvendor model --- Lean Manufacturing --- Industry 4.0 --- economic --- environmental --- and social --- structure equations modeling --- sustainable global supply chain --- single- and multi-objective optimization method --- sustainability design constraint --- software application --- real case study --- pulp and paper industry --- comparative index --- cross-country analysis --- JIT implementation --- suppliers in JIT --- operational benefits --- human factor in JIT --- material flow --- structural equation model --- carbon credit --- environmental cost accounting --- pyrolysis --- solid waste --- vendor selection --- product life cycle --- multi-objective linear programming --- multi-choice goal programming --- additive manufacturing --- social change --- social impacts --- 3D printing --- rapid prototyping --- recycling investment strategy --- demand uncertainty --- Stochastic nonlinear Programming --- Monte-Carlo based sample average approximation method --- memetic algorithm --- industrial symbiosis --- potential industrial symbiosis --- eco-industrial parks --- sustainable supply chain management --- research methods --- scientific production --- metrics --- indicators