Synopsis
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.
About the Author
William H. Asquith, Ph.D., Ph.D., P.G., is both a Research Hydrologist for the U.S. Geological Survey in Lubbock, Texas and an Adjunct Scientist at Texas Tech University. He has earned separate doctorates in Geosciences and Civil Engineering from University of Texas at Austin and Texas Tech University in Lubbock, respectively. He is a registered Professional Geoscientist in Texas and periodically teaches undergraduate and graduate courses. He has more than 20 years of experience in computational and statistical analysis of surface-water resources and various meteorologic phenomena. He has authored or co-authored over 60 publications and various software libraries in the R environment for statistical computing. His interest in L-moments dates from 1995, and the first sketches of the outline of this monograph are dated February 1997. His dissertation in Civil Engineering was parlayed into this monograph. He has considerable interest in a range of statistical topics, R, Perl, MacOSX, the open-source software movement, computational statistics and data mining, scientific illustration, LaTeX, and professional typesetting. Professionally, he also enjoys operating data-acquisition systems, light fabrication, and engineering and geologic field work. In his spare time, he enjoys family, vegetable gardening, cycling, and triathlon.
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