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Gamma And Related Distributions


Gamma And Related Distributions
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Gamma And Related Distributions


Gamma And Related Distributions
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Author : K. Carolynne Ayienda
language : en
Publisher: BoD – Books on Demand
Release Date : 2014-02-27

Gamma And Related Distributions written by K. Carolynne Ayienda and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-27 with Mathematics categories.


The gamma distribution is one of the continuous distributions. Gamma distributions are very versatile and give useful presentations of many physical situations. They are perhaps the most applied statistical distribution in the area of reliability. Gamma distributions are of different types, 1, 2, 3, 4-parameters. They are applied in different fields, among them finance, economics, hydrological and in civil engineering. In this study we have constructed different types of gamma distributions using transformation/change of variable and cumulative techniques and calculated their properties using moments, identified their special cases and calculated their properties too. We have also constructed gamma related distribution using transformation and cumulative techniques and most of these distributions are expressed using special functions, also we have used the gamma-generator and gamma exponetiated–generator to generate new family of distributions.



Handbook Of Exponential And Related Distributions For Engineers And Scientists


Handbook Of Exponential And Related Distributions For Engineers And Scientists
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Author : Nabendu Pal
language : en
Publisher: CRC Press
Release Date : 2005-11-21

Handbook Of Exponential And Related Distributions For Engineers And Scientists written by Nabendu Pal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-21 with Mathematics categories.


The normal distribution is widely known and used by scientists and engineers. However, there are many cases when the normal distribution is not appropriate, due to the data being skewed. Rather than leaving you to search through journal articles, advanced theoretical monographs, or introductory texts for alternative distributions, the Handbook of E



Linear Models And The Relevant Distributions And Matrix Algebra


Linear Models And The Relevant Distributions And Matrix Algebra
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Author : David A. Harville
language : en
Publisher: CRC Press
Release Date : 2023-10-23

Linear Models And The Relevant Distributions And Matrix Algebra written by David A. Harville and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-23 with Mathematics categories.


Linear Models and the Relevant Distributions and Matrix Algebra: A Unified Approach, Volume 2 covers several important topics that were not included in the first volume. The second volume complements the first, providing detailed solutions to the exercises in both volumes, thereby greatly enhancing its appeal for use in advanced statistics programs. This volume can serve as a valuable reference. It can also serve as a resource in a mathematical statistics course for use in illustrating various theoretical concepts in the context of a relatively complex setting of great practical importance. Together with the first volume, this volume provides a largely self-contained treatment of an important area of statistics and should prove highly useful to graduate students and others. Key Features: Includes solutions to the exercises from both the first and second volumes Includes coverage of several topics not covered in the first volume Highly valuable as a reference book for graduate students and researchers



Closure Properties For Heavy Tailed And Related Distributions


Closure Properties For Heavy Tailed And Related Distributions
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Author : Remigijus Leipus
language : en
Publisher: Springer Nature
Release Date : 2023-09-14

Closure Properties For Heavy Tailed And Related Distributions written by Remigijus Leipus and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-14 with Mathematics categories.


This book provides a compact and systematic overview of closure properties of heavy-tailed and related distributions, including closure under tail equivalence, convolution, finite mixing, maximum, minimum, convolution power and convolution roots, and product-convolution closure. It includes examples and counterexamples that give an insight into the theory and provides numerous references to technical details and proofs for a deeper study of the subject. The book will serve as a useful reference for graduate students, young researchers, and applied scientists.



Symmetric Multivariate And Related Distributions


Symmetric Multivariate And Related Distributions
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Author : Kai Wang Fang
language : en
Publisher: CRC Press
Release Date : 2018-01-18

Symmetric Multivariate And Related Distributions written by Kai Wang Fang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-18 with Mathematics categories.


Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.



Continuous Bivariate Distributions


Continuous Bivariate Distributions
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Author : N. Balakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-31

Continuous Bivariate Distributions written by N. Balakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-31 with Mathematics categories.


Along with a review of general developments relating to bivariate distributions, this volume also covers copulas, a subject which has grown immensely in recent years. In addition, it examines conditionally specified distributions and skewed distributions.



Quantitative Ultrasound In Soft Tissues


Quantitative Ultrasound In Soft Tissues
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Author : Jonathan Mamou
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-26

Quantitative Ultrasound In Soft Tissues written by Jonathan Mamou and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Medical categories.


Due to parallel advances in signal processing and computer hardware in the last 15 years, quantitative ultrasound techniques have reached maturity, allowing for the construction of quantitative maps or images of soft tissues. This book will focus on 5 modern research topics related to quantitative ultrasound of soft tissues: - Spectral-based methods for tissue characterization, tissue typing, cancer detection, etc.; - Envelope statistics analysis as a means of quantifying and imaging tissue properties; - Ultrasound elastography for quantifying elastic properties of tissues (several clinical ultrasound scanners now display elastography images); - Scanning acoustic microscopy for forming images of mechanical properties of soft tissues with micron resolution (desktop size scanners are now available); and - Ultrasound computer tomography for breast cancer imaging (new ultrasound tomography systems have been developed and are currently under evaluation clinically).



Continuous Univariate Distributions Volume 2


Continuous Univariate Distributions Volume 2
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Author : Norman L. Johnson
language : en
Publisher: John Wiley & Sons
Release Date : 1995-05-08

Continuous Univariate Distributions Volume 2 written by Norman L. Johnson 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 1995-05-08 with Mathematics categories.


Comprehensive reference for statistical distributions Continuous Univariate Distributions, Volume 2 provides in-depth reference for anyone who applies statistical distributions in fields including engineering, business, economics, and the sciences. Covering a range of distributions, both common and uncommon, this book includes guidance toward extreme value, logistics, Laplace, beta, rectangular, noncentral distributions and more. Each distribution is presented individually for ease of reference, with clear explanations of methods of inference, tolerance limits, applications, characterizations, and other important aspects, including reference to other related distributions.



Learning Bayesian Models With R


Learning Bayesian Models With R
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Author : Dr. Hari M. Koduvely
language : en
Publisher: Packt Publishing Ltd
Release Date : 2015-10-28

Learning Bayesian Models With R written by Dr. Hari M. Koduvely and has been published by Packt Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-28 with Computers categories.


Become an expert in Bayesian Machine Learning methods using R and apply them to solve real-world big data problems About This Book Understand the principles of Bayesian Inference with less mathematical equations Learn state-of-the art Machine Learning methods Familiarize yourself with the recent advances in Deep Learning and Big Data frameworks with this step-by-step guide Who This Book Is For This book is for statisticians, analysts, and data scientists who want to build a Bayes-based system with R and implement it in their day-to-day models and projects. It is mainly intended for Data Scientists and Software Engineers who are involved in the development of Advanced Analytics applications. To understand this book, it would be useful if you have basic knowledge of probability theory and analytics and some familiarity with the programming language R. What You Will Learn Set up the R environment Create a classification model to predict and explore discrete variables Get acquainted with Probability Theory to analyze random events Build Linear Regression models Use Bayesian networks to infer the probability distribution of decision variables in a problem Model a problem using Bayesian Linear Regression approach with the R package BLR Use Bayesian Logistic Regression model to classify numerical data Perform Bayesian Inference on massively large data sets using the MapReduce programs in R and Cloud computing In Detail Bayesian Inference provides a unified framework to deal with all sorts of uncertainties when learning patterns form data using machine learning models and use it for predicting future observations. However, learning and implementing Bayesian models is not easy for data science practitioners due to the level of mathematical treatment involved. Also, applying Bayesian methods to real-world problems requires high computational resources. With the recent advances in computation and several open sources packages available in R, Bayesian modeling has become more feasible to use for practical applications today. Therefore, it would be advantageous for all data scientists and engineers to understand Bayesian methods and apply them in their projects to achieve better results. Learning Bayesian Models with R starts by giving you a comprehensive coverage of the Bayesian Machine Learning models and the R packages that implement them. It begins with an introduction to the fundamentals of probability theory and R programming for those who are new to the subject. Then the book covers some of the important machine learning methods, both supervised and unsupervised learning, implemented using Bayesian Inference and R. Every chapter begins with a theoretical description of the method explained in a very simple manner. Then, relevant R packages are discussed and some illustrations using data sets from the UCI Machine Learning repository are given. Each chapter ends with some simple exercises for you to get hands-on experience of the concepts and R packages discussed in the chapter. The last chapters are devoted to the latest development in the field, specifically Deep Learning, which uses a class of Neural Network models that are currently at the frontier of Artificial Intelligence. The book concludes with the application of Bayesian methods on Big Data using the Hadoop and Spark frameworks. Style and approach The book first gives you a theoretical description of the Bayesian models in simple language, followed by details of its implementation in the R package. Each chapter has illustrations for the use of Bayesian model and the corresponding R package, using data sets from the UCI Machine Learning repository. Each chapter also contains sufficient exercises for you to get more hands-on practice.



Statistical Size Distributions In Economics And Actuarial Sciences


Statistical Size Distributions In Economics And Actuarial Sciences
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Author : Christian Kleiber
language : en
Publisher: John Wiley & Sons
Release Date : 2003-10-24

Statistical Size Distributions In Economics And Actuarial Sciences written by Christian Kleiber 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 2003-10-24 with Mathematics categories.


A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.