Distributional Analysis with L-moment Statistics Using the R Environment for Statistical Computing PDF Download

Author: William H. Asquith
Publisher: Createspace Independent Publishing Platform
ISBN: 9781463508418
Category : L-moments
Languages : en
Pages : 0

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Book Description
This monograph (2nd printing) is the most complete account to date of L-moment statistics in the context of distributional analysis using an open-source programming environment-the R environment for statistical computing. The target audience are engineers/scientists with limited backgrounds in statistics and computer programming but with responsibilities in analyzing highly non-Normal, skewed, or heavy-tailed data. The monograph is written in continuous narrative and is oriented around the software package "lmomco" previously written by the author but tremendously expanded and refined for the monograph. The monograph covers an introduction to R and cites the extensive book-literature on computational and statistical analysis using R. Note, an errata can be found in the text file ERRATA_FOR_ISBN9781463508418.txt that is distributed with the lmomco package.The monograph covers, by a large-scale coupling of source code to typeset mathematics, a myriad of topics including quantile functions, order statistics, product moments, probability-weighted moments (PWMs), censored PWMs, L-moments (censored/trimmed), L-comoments, and numerous probability distributions including the two-parameter Cauchy, Exponential, Normal, Gamma, Gumbel, reverse Gumbel, Kumaraswamy, Rayleigh, and Rice; the three-parameter Generalized Extreme Value, Generalized Logistic, Generalized Normal, Generalized Pareto (GPA), right-censored (RC) GPA, trimmed GPA, Pearson Type III, and Weibull; four- and more parameter distributions including the Kappa, Generalized Lambda (GLD), trimmed GLD, and Wakeby; and the method of L-moments and method of PWMs for these distributions.The monograph thoroughly describes L-moment ratio diagrams. Venerable statistics such as Sen weighted mean and Gini mean difference also are considered as are emergent statistical functions such as copulas. Extensive simulation studies are shown through code examples and the results are often depicted in figures; these studies demonstrate the reliability of the examples and lmomco by demonstrating consistency with results with the literature. Topical case studies of regional distributional analysis of hydrometeorologic data are shown to guide readers.The monograph presents new developments by the author or following prior literature results that include censored PWMs and L-moments by censoring fraction, threshold, and indicator; the Cauchy, Kumaraswamy, Rayleigh, Rice, trimmed GPA, and RC-GPA distributions; L-comoments in context of copulas; and theoretical (non-sample) computation of L-moments.The monograph provides more than 245 code examples, about 515 numbered equations, a thorough topical index, and an index of about 425 R functions used in the examples. Approximately 100 figures are provided and virtually all of the figures can be created from the code in the text.

Author: W. Asquith
Publisher:
ISBN: 9781500180935
Category :
Languages : en
Pages : 500

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Book Description
Data have sample distributions. Analysis of these data is a complex subject, which is simultaneously influenced by, and has influence in, many branches of statistics and other disciplines. The literature of distributions is extensive, and disciplines requiring distributions are encompassing. L-moments provide a powerful and easy to use statistical framework for distributional analysis.The theory of L-moments as implemented by the R package lmomco includes computation of L-moments, trimmed L-moments, methods for L-moment computation for distributions and estimation from samples, inclusion of probability-weighted moments, sample properties of both moment types, parameter estimation methods for numerous familiar and not-so-familiar distributions, techniques for discriminating between distributions, and numerous other topics related to L-moments and quantile functions.What are L-moments? To answer succinctly, L-moments are defined through linear combinations of the expected values of order statistics. The study of order statistics is a branch of statistics concerned with the statistics of ordered random variables and samples. The familiar minimum, maximum, and median are likely the most familiar order statistics.L-moments are direct analogs-but not numerically equivalent-to well-known product moments, such as standard deviation or skew. The first L-moment is the arithmetic mean, which should be particularly comforting to readers who are not previously familiar with L-moments. As analogs, L-moments have similar, that is, familiar, interpretations and hence applications as the product moments. L-moments, therefore, are useful and are intellectually accessible to most of the general scientific and engineering community. Accessibility into L-moment theory is greatly enhanced in practical application by the L-moment support available in R such as provided by the lmomco package.This book is a special rendering of the user manual for research software package "lmomco." That package and documentation is openly available on the Comprehensive R Archive Network (CRAN). The CRAN is the central repository of contributed extensions to the R Environment for Statistical Computing.The lmomco package is a comparatively comprehensive implementation of the theory of L-moments in addition to probability-weighted moments, and parameter estimation for numerous familiar and not-so-familiar distributions. Over 330 user-level functions are implemented that range from low-level utilities forming an API to high-level sophisticated data analysis and visualization operators.This book is for the version series 2.1+ of lmomco and represents a milestone release following detailed auditing against the rigorous mathematical and programming text "Distributional Analysis with L-moment Statistics using the R Environment for Statistical Computing" also published by the author (ISBN 978-146350841-8).

Author: Maria L. Rizzo
Publisher: CRC Press
ISBN: 1420010719
Category : Reference
Languages : en
Pages : 412

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Book Description
Computational statistics and statistical computing are two areas that employ computational, graphical, and numerical approaches to solve statistical problems, making the versatile R language an ideal computing environment for these fields. One of the first books on these topics to feature R, Statistical Computing with R covers the traditiona

Author: Yosef Cohen
Publisher: John Wiley & Sons
ISBN: 047072188X
Category : Mathematics
Languages : en
Pages : 618

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Book Description
R, an Open Source software, has become the de facto statistical computing environment. It has an excellent collection of data manipulation and graphics capabilities. It is extensible and comes with a large number of packages that allow statistical analysis at all levels – from simple to advanced – and in numerous fields including Medicine, Genetics, Biology, Environmental Sciences, Geology, Social Sciences and much more. The software is maintained and developed by academicians and professionals and as such, is continuously evolving and up to date. Statistics and Data with R presents an accessible guide to data manipulations, statistical analysis and graphics using R. Assuming no previous knowledge of statistics or R, the book includes: A comprehensive introduction to the R language. An integrated approach to importing and preparing data for analysis, exploring and analyzing the data, and presenting results. Over 300 examples, including detailed explanations of the R scripts used throughout. Over 100 moderately large data sets from disciplines ranging from Biology, Ecology and Environmental Science to Medicine, Law, Military and Social Sciences. A parallel discussion of analyses with the normal density, proportions (binomial), counts (Poisson) and bootstrap methods. Two extensive indexes that include references to every R function (and its arguments and packages used in the book) and to every introduced concept.

Author: G. Jay Kerns
Publisher: Lulu.com
ISBN: 0557249791
Category : Education
Languages : en
Pages : 388

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Book Description
This is a textbook for an undergraduate course in probability and statistics. The approximate prerequisites are two or three semesters of calculus and some linear algebra. Students attending the class include mathematics, engineering, and computer science majors.

Author: Zaven A. Karian
Publisher: CRC Press
ISBN: 1584887125
Category : Mathematics
Languages : en
Pages : 1722

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Book Description
With the development of new fitting methods, their increased use in applications, and improved computer languages, the fitting of statistical distributions to data has come a long way since the introduction of the generalized lambda distribution (GLD) in 1969. Handbook of Fitting Statistical Distributions with R presents the latest and best methods

Author: Torsten Hothorn
Publisher: Chapman and Hall/CRC
ISBN: 9781420079333
Category : Mathematics
Languages : en
Pages : 376

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Book Description
A Proven Guide for Easily Using R to Effectively Analyze Data Like its bestselling predecessor, A Handbook of Statistical Analyses Using R, Second Edition provides a guide to data analysis using the R system for statistical computing. Each chapter includes a brief account of the relevant statistical background, along with appropriate references. New to the Second Edition New chapters on graphical displays, generalized additive models, and simultaneous inference A new section on generalized linear mixed models that completes the discussion on the analysis of longitudinal data where the response variable does not have a normal distribution New examples and additional exercises in several chapters A new version of the HSAUR package (HSAUR2), which is available from CRAN This edition continues to offer straightforward descriptions of how to conduct a range of statistical analyses using R, from simple inference to recursive partitioning to cluster analysis. Focusing on how to use R and interpret the results, it provides students and researchers in many disciplines with a self-contained means of using R to analyze their data.

Author: Torsten Hothorn
Publisher: CRC Press
ISBN: 1482204592
Category : Mathematics
Languages : en
Pages : 447

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Book Description
Like the best-selling first two editions, A Handbook of Statistical Analyses using R, Third Edition provides an up-to-date guide to data analysis using the R system for statistical computing. The book explains how to conduct a range of statistical analyses, from simple inference to recursive partitioning to cluster analysis.New to the Third Edition

Author: Joseph Schmuller
Publisher: John Wiley & Sons
ISBN: 1119337267
Category : Computers
Languages : en
Pages : 480

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Book Description
Understanding the world of R programming and analysis has never been easier Most guides to R, whether books or online, focus on R functions and procedures. But now, thanks to Statistical Analysis with R For Dummies, you have access to a trusted, easy-to-follow guide that focuses on the foundational statistical concepts that R addresses—as well as step-by-step guidance that shows you exactly how to implement them using R programming. People are becoming more aware of R every day as major institutions are adopting it as a standard. Part of its appeal is that it's a free tool that's taking the place of costly statistical software packages that sometimes take an inordinate amount of time to learn. Plus, R enables a user to carry out complex statistical analyses by simply entering a few commands, making sophisticated analyses available and understandable to a wide audience. Statistical Analysis with R For Dummies enables you to perform these analyses and to fully understand their implications and results. Gets you up to speed on the #1 analytics/data science software tool Demonstrates how to easily find, download, and use cutting-edge community-reviewed methods in statistics and predictive modeling Shows you how R offers intel from leading researchers in data science, free of charge Provides information on using R Studio to work with R Get ready to use R to crunch and analyze your data—the fast and easy way!

Author: Arthur Pewsey
Publisher:
ISBN: 0199671133
Category : Computers
Languages : en
Pages : 198

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Book Description
Measurements like mass, length and speed are "linear"; but compass direction or the time of the year are "circular". Circular data have a repeating nature and an arbitrary zero: 12 months after the 1st of July it is the 1st of July again. This book explains how to easily and effectively analyse circular data statistically.