Author

# J. Maciunas Landwehr

Bio: J. Maciunas Landwehr is an academic researcher. The author has contributed to research in topics: Quantile & L-moment. The author has an hindex of 6, co-authored 8 publications receiving 1734 citations.

Topics: Quantile, L-moment, Estimator, K-distribution, Minimax estimator

##### 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

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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 authors examined the statistical properties of historical and simulated flood sequences in real and log space and found that the construction and use of regional skew maps in log space are most likely counterproductive.

Abstract: Some statistics of historical and simulated flood sequences were examined in real and log space. It was found that several statistical properties of floods in real space could not be inferred from those in log space without extensive knowledge of the distribution of floods in real space as well as information about their sampling characteristics. It is shown that the construction and use of regional skew maps in log space are most likely counterproductive.

105 citations

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TL;DR: In this paper, an algorithm based on the use of probability weighted moments allows estimation of the parameters, hence quantiles, of the Wakeby distribution, for the case where the lower bound is not known.

Abstract: An algorithm based on the use of probability weighted moments allows estimation of the parameters, hence quantiles, of the Wakeby distribution. For the case where the lower bound is not known, the performance of the algorithm using unbiased estimates of the probability weighted moments is compared to that using biased estimates. The choice of estimating algorithm, determined as that which minimizes the root mean square error of the quantiles, appears to be unimportant when the upper (flood) quantiles are of interest and the lower bound is not known, in contrast to the lower (drought) quantiles.

102 citations

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TL;DR: The desirable properties of an estimator relative to a hypothetical population may be irrelevant in practice unless the population at issue more or less resembles the hypothetical population as mentioned in this paper, which may not be the case in practice.

Abstract: The desirable properties of an estimator relative to a hypothetical population may be irrelevant in practice unless the population at issue more or less resembles the hypothetical population. Evidence that floods are distributed with long, stretched upper tails suggests that use of the more common distributions results in a rather precise underestimation of the extreme quantiles and thereby in the underdesign of flood protection measures.

75 citations

##### Cited by

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IBM

^{1}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

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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

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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

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IBM

^{1}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

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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