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.