Distributions For Modeling Location Scale And Shape
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Distributions For Modeling Location Scale And Shape
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Author : Robert A. Rigby
language : en
Publisher: CRC Press
Release Date : 2019-10-08
Distributions For Modeling Location Scale And Shape written by Robert A. Rigby and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-08 with Mathematics categories.
This is a book about statistical distributions, their properties, and their application to modelling the dependence of the location, scale, and shape of the distribution of a response variable on explanatory variables. It will be especially useful to applied statisticians and data scientists in a wide range of application areas, and also to those interested in the theoretical properties of distributions. This book follows the earlier book ‘Flexible Regression and Smoothing: Using GAMLSS in R’, [Stasinopoulos et al., 2017], which focused on the GAMLSS model and software. GAMLSS (the Generalized Additive Model for Location, Scale, and Shape, [Rigby and Stasinopoulos, 2005]), is a regression framework in which the response variable can have any parametric distribution and all the distribution parameters can be modelled as linear or smooth functions of explanatory variables. The current book focuses on distributions and their application. Key features: Describes over 100 distributions, (implemented in the GAMLSS packages in R), including continuous, discrete and mixed distributions. Comprehensive summary tables of the properties of the distributions. Discusses properties of distributions, including skewness, kurtosis, robustness and an important classification of tail heaviness. Includes mixed distributions which are continuous distributions with additional specific values with point probabilities. Includes many real data examples, with R code integrated in the text for ease of understanding and replication. Supplemented by the gamlss website. This book will be useful for applied statisticians and data scientists in selecting a distribution for a univariate response variable and modelling its dependence on explanatory variables, and to those interested in the properties of distributions.
Generalized Additive Models For Location Scale And Shape
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Author : Mikis D. Stasinopoulos
language : en
Publisher:
Release Date : 2024
Generalized Additive Models For Location Scale And Shape written by Mikis D. Stasinopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Regression analysis categories.
"This text provides a state-of-the-art treatment of distributional regression, accompanied by real-world examples from diverse areas of application. Maximum likelihood, Bayesian and machine learning approaches are covered in-depth and contrasted, providing an integrated perspective on GAMLSS for researchers in statistics and other data-rich fields"--
Flexible Regression And Smoothing
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Author : Mikis D. Stasinopoulos
language : en
Publisher: CRC Press
Release Date : 2017-04-21
Flexible Regression And Smoothing written by Mikis D. Stasinopoulos and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-21 with Mathematics categories.
This book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. In particular, the GAMLSS statistical framework enables flexible regression and smoothing models to be fitted to the data. The GAMLSS model assumes that the response variable has any parametric (continuous, discrete or mixed) distribution which might be heavy- or light-tailed, and positively or negatively skewed. In addition, all the parameters of the distribution (location, scale, shape) can be modelled as linear or smooth functions of explanatory variables. Key Features: Provides a broad overview of flexible regression and smoothing techniques to learn from data whilst also focusing on the practical application of methodology using GAMLSS software in R. Includes a comprehensive collection of real data examples, which reflect the range of problems addressed by GAMLSS models and provide a practical illustration of the process of using flexible GAMLSS models for statistical learning. R code integrated into the text for ease of understanding and replication. Supplemented by a website with code, data and extra materials. This book aims to help readers understand how to learn from data encountered in many fields. It will be useful for practitioners and researchers who wish to understand and use the GAMLSS models to learn from data and also for students who wish to learn GAMLSS through practical examples.
Some Bivariate Distributions For Modeling The Strength Properties Of Lumber
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Author : Richard Arnold Johnson
language : en
Publisher:
Release Date : 1999
Some Bivariate Distributions For Modeling The Strength Properties Of Lumber written by Richard Arnold Johnson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Distribution (Probability theory) categories.
Accurate modeling of the joint stochastic nature of the strength properties of dimension lumber is essential to the determination of reliability-based design safety factors. This report reviews the major techniques for obtaining bivariate distributions and then discusses bivariate distributions whose marginal distributions suggest they might be useful for modeling the joint distribution of two strength properties. Finally, we pick a bivariate Weibull distribution and show that we can write its likelihood function under a proof loading scheme, offering the possibility that it can be used to model the joint distribution of two properties that must each be measured using a destructive test.
Statistical Distributions
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Author : Nick T. Thomopoulos
language : en
Publisher: Springer
Release Date : 2017-10-10
Statistical Distributions written by Nick T. Thomopoulos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-10 with Mathematics categories.
This book gives a description of the group of statistical distributions that have ample application to studies in statistics and probability. Understanding statistical distributions is fundamental for researchers in almost all disciplines. The informed researcher will select the statistical distribution that best fits the data in the study at hand. Some of the distributions are well known to the general researcher and are in use in a wide variety of ways. Other useful distributions are less understood and are not in common use. The book describes when and how to apply each of the distributions in research studies, with a goal to identify the distribution that best applies to the study. The distributions are for continuous, discrete, and bivariate random variables. In most studies, the parameter values are not known a priori, and sample data is needed to estimate parameter values. In other scenarios, no sample data is available, and the researcher seeks some insight that allows the estimate of the parameter values to be gained. This handbook of statistical distributions provides a working knowledge of applying common and uncommon statistical distributions in research studies. These nineteen distributions are: continuous uniform, exponential, Erlang, gamma, beta, Weibull, normal, lognormal, left-truncated normal, right-truncated normal, triangular, discrete uniform, binomial, geometric, Pascal, Poisson, hyper-geometric, bivariate normal, and bivariate lognormal. Some are from continuous data and others are from discrete and bivariate data. This group of statistical distributions has ample application to studies in statistics and probability and practical use in real situations. Additionally, this book explains computing the cumulative probability of each distribution and estimating the parameter values either with sample data or without sample data. Examples are provided throughout to guide the reader. Accuracy in choosing and applying statistical distributions is particularly imperative for anyone who does statistical and probability analysis, including management scientists, market researchers, engineers, mathematicians, physicists, chemists, economists, social science researchers, and students in many disciplines.
Weibull Models
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Author : D. N. Prabhakar Murthy
language : en
Publisher: John Wiley & Sons
Release Date : 2004-01-28
Weibull Models written by D. N. Prabhakar Murthy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-28 with Mathematics categories.
A comprehensive perspective on Weibull models The literature on Weibull models is vast, disjointed, andscattered across many different journals. Weibull Models is acomprehensive guide that integrates all the different facets ofWeibull models in a single volume. This book will be of great help to practitioners in reliabilityand other disciplines in the context of modeling data sets usingWeibull models. For researchers interested in these modelingtechniques, exercises at the end of each chapter define potentialtopics for future research. Organized into seven distinct parts, Weibull Models: * Covers model analysis, parameter estimation, model validation,and application * Serves as both a handbook and a research monograph. As ahandbook, it classifies the different models and presents theirproperties. As a research monograph, it unifies the literature andpresents the results in an integrated manner * Intertwines theory and application * Focuses on model identification prior to model parameterestimation * Discusses the usefulness of the Weibull Probability plot (WPP)in the model selection to model a given data set * Highlights the use of Weibull models in reliability theory Filled with in-depth analysis, Weibull Models pulls together themost relevant information on this topic to give everyone fromreliability engineers to applied statisticians involved withreliability and survival analysis a clear look at what Weibullmodels can offer.
Statistical Distributions
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Author : Catherine Forbes
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-21
Statistical Distributions written by Catherine Forbes and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-21 with Mathematics categories.
A new edition of the trusted guide on commonly used statistical distributions Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis. Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features: A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems Methods for extending independent modeling schemes to the dependent case, covering techniques for generating complex distributions from simple distributions New coverage of conditional probability, including conditional expectations and joint and marginal distributions Commonly used tables associated with the normal (Gaussian), student-t, F and chi-square distributions Additional reviewing methods for the estimation of unknown parameters, such as the method of percentiles, the method of moments, maximum likelihood inference, and Bayesian inference Statistical Distributions, Fourth Edition is an excellent supplement for upper-undergraduate and graduate level courses on the topic. It is also a valuable reference for researchers and practitioners in the fields of engineering, economics, operations research, and the social sciences who conduct statistical analyses.
Extreme Value Modeling And Risk Analysis
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Author : Dipak K. Dey
language : en
Publisher: CRC Press
Release Date : 2016-01-06
Extreme Value Modeling And Risk Analysis written by Dipak K. Dey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-06 with Mathematics categories.
Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subje
Six Sigma Distribution Modeling
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Author : Andrew Sleeper
language : en
Publisher: McGraw Hill Professional
Release Date : 2007-01-09
Six Sigma Distribution Modeling written by Andrew Sleeper and has been published by McGraw Hill Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-09 with Technology & Engineering categories.
Publisher's Note: Products purchased from Third Party sellers are not guaranteed by the publisher for quality, authenticity, or access to any online entitlements included with the product. Sleeper provides six sigma practitioners with the tools which will allow them to stand out from your competitors by using advanced statistical and modeling tools for more in-depth analysis. Understanding and properly utilizing statistical data distributions is one of the most important and difficult skills for a six sigma practitioner to possess. Sleeper provides six sigma practitioners with a road map for selecting and using distributions for more precise outcomes. With the added value of Crystal Ball Modeling software, this book becomes a powerful tool for analyzing and modeling difficult data quickly and efficiently.
Univariate Stable Distributions
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Author : John P. Nolan
language : en
Publisher: Springer Nature
Release Date : 2020-09-13
Univariate Stable Distributions written by John P. Nolan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-13 with Mathematics categories.
This textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios. Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice. Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.