<i>L</i>moment diagrams should replace product moment diagrams

Vogel, Richard M.; Fennessey, Neil M.

doi:10.1029/93wr00341

Cited by 386 publications

(238 citation statements)

References 14 publications

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“…They are commonly estimated by the method of moments (Chow, 1964;Rao and Hamed, 2000), although they can also be estimated by L-moments (Greenwood et al, 1979). The method of L-moments was preferred here because it yields more robust estimations than conventional moments (Vogel and Fennessey, 1993;Sankarasubramanian and Srinivasan, 1999). Hosking (1990) explains in detail the estimation of parameters using L-moments.…”

Section: Extreme Dry-spell Modelling With Annual Maximum Series and Gmentioning

confidence: 99%

Estimating extreme dry‐spell risk in the middle Ebro valley (northeastern Spain): a comparative analysis of partial duration series with a general Pareto distribution and annual maxima series with a Gumbel distribution

Vicente‐Serrano

Beguería

2003

Intl Journal of Climatology

102

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This paper analyses a 50 year time series of daily precipitation in a region of the middle Ebro valley (northeastern Spain) in order to predict extreme dry-spell risk. A comparison of observed and estimated maximum dry spells (50 year return period) showed that the generalized Pareto (GP) distribution combined with partial duration series (PDS) gives better results than the Gumbel distribution fitted to annual maximum series. Indeed, the classical Gumbel approach underestimated the empirical duration of dry spells. The PDS-GP approach was successfully applied in the study of extreme hydro-climatic variable values. The results reported here could be applied in estimating climatic drought risks in other geographical areas.

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Section: Extreme Dry-spell Modelling With Annual Maximum Series and Gmentioning

confidence: 99%

Estimating extreme dry‐spell risk in the middle Ebro valley (northeastern Spain): a comparative analysis of partial duration series with a general Pareto distribution and annual maxima series with a Gumbel distribution

Vicente‐Serrano

Beguería

2003

Intl Journal of Climatology

102

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“…On the same plot, the theoretical relationships for various probability density functions are compared to the observations. Vogel and Fennessey (1993) have shown that L-moment ratio diagrams are nearly always an improvement over ordinary moment ratio diagrams because L-moment ratios are approximately unbiased, whereas ordinary moment ratios can exhibit enormous downward bias, particularly for skewed samples, even with extremely large samples. Hosking (1990), Stedinger et al (1993), Hosking and Wallis (1997), and others have summarized the theory of L-moments, thus we do not reproduce the theory here.…”

Section: The Theory Of L-momentsmentioning

confidence: 99%

Goodness of Fit of Probability Distributions for Sightings as Species Approach Extinction

et al. 2009

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Estimating the probability that a species is extinct and the timing of extinctions is useful in biological fields ranging from paleoecology to conservation biology. Various statistical methods have been introduced to infer the time of extinction and extinction probability from a series of individual sightings. There is little evidence, however, as to which of these models provide adequate fit to actual sighting records. We use L-moment diagrams and probability plot correlation coefficient (PPCC) hypothesis tests to evaluate the goodness of fit of various probabilistic models to sighting data collected for a set of North American and Hawaiian bird populations that have either gone extinct, or are suspected of having gone extinct, during the past 150 years. For our data, the uniform, truncated exponential, and generalized Pareto models performed moderately well, but the Weibull model performed poorly. Of the acceptable models, the uniform distribution performed best based on PPCC goodness of fit comparisons and sequential Bonferroni-type tests. Further analyses using field significance tests suggest that although the uniform distribution is the best of those considered, additional work remains to evaluate the truncated exponential model more fully. The methods we present here provide a framework for evaluating subsequent models.

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“…LH-moments are the extension or generalization of L-moments, which are defi ned as the linear combination of higher order statistics introduced by Wang [12]. Product moments and moment ratios have been found to be sensitive to the upper part of distributions and thus sample outliers [39]. The L moments are oversensitive to the lower part of distributions and give insuffi cient weight to large sample values that actually contain useful information on the upper distribution tail [12].…”

Section: Methodsmentioning

confidence: 99%

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

Ahmad

Abbass²,

Saghir

et al. 2016

Pol. J. Environ. Stud.

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In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fi t (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offi t (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fi t distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.

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Lmoment diagrams should replace product moment diagrams

Cited by 386 publications

References 14 publications

Estimating extreme dry‐spell risk in the middle Ebro valley (northeastern Spain): a comparative analysis of partial duration series with a general Pareto distribution and annual maxima series with a Gumbel distribution

Estimating extreme dry‐spell risk in the middle Ebro valley (northeastern Spain): a comparative analysis of partial duration series with a general Pareto distribution and annual maxima series with a Gumbel distribution

Goodness of Fit of Probability Distributions for Sightings as Species Approach Extinction

Finding Probability Distributions for Annual Daily Maximum Rainfall in Pakistan Using Linear Moments and Variants

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