Author
N. C. Matalas
Bio: N. C. Matalas is an academic researcher from United States Department of the Interior. The author has contributed to research in topics: Skewness & Gumbel distribution. The author has an hindex of 17, co-authored 27 publications receiving 2683 citations.
Papers
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TL;DR: In this article, Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions, such as Tukey's lambda, which may present problems in deriving their parameters by more conventional means.
Abstract: Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.
1,147 citations
TL;DR: In this paper, estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared.
Abstract: Estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared. Results were derived from Monte Carlo experiments by using both independent and serially correlated Gumbel numbers. The method of probability weighted moments was seen to compare favorably with the other two techniques.
412 citations
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TL;DR: In this paper, the distribution functions for three statistics, the mean, standard deviation, and coefficient of skewness, for small samples from various distributions were obtained by Monte Carlo experiments, and sample sizes of 10 (10) 90 were considered, and the distributions used were the normal, Gumbel (extreme value type 1), log normal, Pearson type 3 (gamma), Weibull, and Pareto type 1 (Pearson type 4).
Abstract: The distribution functions for three statistics, the mean, standard deviation, and coefficient of skewness, for small samples from various distributions were obtained by Monte Carlo experiments. Sample sizes of 10 (10) 90 were considered, and the distributions used were the normal, Gumbel (extreme value type 1), log normal, Pearson type 3 (gamma), Weibull, and Pareto type 1 (Pearson type 4). Values of the coefficient of skewness used in generating the samples were in the range [0.0, 15.0]. Pronounced skews, biases, and constraints in the sampling properties of the statistics were observed. Examples of the available graphs of the distribution functions are presented.
189 citations
TL;DR: In this article, the authors describe a modern interdisciplinary science of hydrology needed to develop an in-depth understanding of the connectedness between human and natural systems and to determine effective solutions to resolve the complex water problems that the world faces today.
Abstract: We live in a world where biophysical and social processes are tightly coupled. Hydrologic systems change in response to a variety of natural and human forces such as climate variability and change, water use and water infrastructure, and land cover change. In turn, changes in hydrologic systems impact socioeconomic, ecological, and climate systems at a number of scales, leading to a coevolution of these interlinked systems. The Harvard Water Program, Hydrosociology, Integrated Water Resources Management, Ecohydrology, Hydromorphology, and Sociohydrology were all introduced to provide distinct, interdisciplinary perspectives on water problems to address the contemporary dynamics of human interaction with the hydrosphere and the evolution of the Earth's hydrologic systems. Each of them addresses scientific, social, and engineering challenges related to how humans influence water systems and vice versa. There are now numerous examples in the literature of how holistic approaches can provide a structure and vision of the future of hydrology. We review selected examples, which taken together, describe the type of theoretical and applied integrated hydrologic analyses and associated curricular content required to address the societal issue of water resources sustainability. We describe a modern interdisciplinary science of hydrology needed to develop an in-depth understanding of the dynamics of the connectedness between human and natural systems and to determine effective solutions to resolve the complex water problems that the world faces today. Nearly, every theoretical hydrologic model introduced previously is in need of revision to accommodate how climate, land, vegetation, and socioeconomic factors interact, change, and evolve over time.
160 citations
TL;DR: In this paper, seasonal differences in long-term persistence (h > 0.5) were found for 25 streams in the Potomac River basin, and two statistics, H and K, used as estimators of h were found to have differing small sample properties.
Abstract: Seasonal differences in long-term persistence (h > 0.5), were found for 25 streams in the Potomac River basin. Two statistics, H and K, used as estimators of h were found to have differing small sample properties. K was found to have less variance but a greater positive bias than H. However, the Hurst phenomenon, in which H and K values differ from the expected values for independent series, was confirmed for the Potomac River basin streamflows. Neither marginal distribution nor biased transience appear to be viable explanations for the differences between observed and independent or short memory simulated sequences. For the Potomac basin, the explanation of h > 0.5 can only be attributed to the nature of the correlation structure of the observed series.
134 citations
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IBM1
TL;DR: The authors define L-moments as the expectations of certain linear combinations of order statistics, which can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions.
Abstract: L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves such established procedures as the use of order statistics and Gini's mean difference statistic, and gives rise to some promising innovations such as the measures of skewness and kurtosis and new methods of parameter estimation
2,668 citations
TL;DR: In this paper, the authors review the current state of science regarding historical trends in hydrologic variables, including precipitation, runoff, tropospheric water vapor, soil moisture, glacier mass balance, evaporation and growing season length.
2,025 citations
TL;DR: In this article, statistical downscaling of hydrologic extremes is considered, and future challenges such as the development of more rigorous statistical methodology for regional analysis of extremes, as well as the extension of Bayesian methods to more fully quantify uncertainty in extremal estimation are reviewed.
1,458 citations
TL;DR: In this paper, the authors use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution, and investigate the properties of these estimators in large samples via asymptotic theory, and in small and moderate samples, via computer simulation.
Abstract: We use the method of probability-weighted moments to derive estimators of the parameters and quantiles of the generalized extreme-value distribution. We investigate the properties of these estimators in large samples, via asymptotic theory, and in small and moderate samples, via computer simulation. Probability-weighted moment estimators have low variance and no severe bias, and they compare favorably with estimators obtained by the methods of maximum likelihood or sextiles. The method of probability-weighted moments also yields a convenient and powerful test of whether an extreme-value distribution is of Fisher-Tippett Type I, II, or III.
1,275 citations
IBM1
TL;DR: In this paper, the authors show that unless the sample size is 500 or more, estimators derived by either the method of moments or probability-weighted moments are more reliable.
Abstract: The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including reliability studies and the analysis of environmental extreme events. Maximum likelihood estimation of the generalized Pareto distribution has previously been considered in the literature, but we show, using computer simulation, that, unless the sample size is 500 or more, estimators derived by the method of moments or the method of probability-weighted moments are more reliable. We also use computer simulation to assess the accuracy of confidence intervals for the parameters and quantiles of the generalized Pareto distribution.
1,233 citations