Comparison of three different methods of moments for derivation of probability distribution parameters

Najafian, G.

doi:10.1016/j.apor.2010.06.001

Cited by 9 publications

(6 citation statements)

References 27 publications

(31 reference statements)

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“…(8), the weight func tions in the Gaussian case become of the form of the following equations: The estimation of the L-moments from a sample of size n from the random variable Y is discussed in Ref. [8]. Commonly used estimates are presented in the following equations:…”

Section: Derivation Of Distribution Parameters By L-momentsmentioning

confidence: 99%

“…As the main source of nonlinearity comes from Morison's equation, the parameter y2, the kurtosis coefficient of the response sampled time history, has been com puted by an approximation proposed by Najafian [8], As can be seen in Ref. [8], Eq. (40) showed to be much more efficient than conventional method of moments for high-kurtosis distributions …”

Section: Is Tr Ib U Tio N S O F T H E P Ro C E S S P E a K S A mentioning

confidence: 99%

“…The statistical equivalence between y(t) and a standard Gaussian time series u(t) is expressed by the following equation: Although the methodology presented by Winterstein and McKenzie [11] for L-Hermite coefficients, feasible results for this specific application were not obtained and among the possibilities, the methodology applied in this work proposes that the coeffi cients c3 and c4 be computed through standard numerical procedures preserving original skewness coefficient and applying L-kurtosis instead of kurtosis. As the main source of nonlinearity comes from Morison's equation, the parameter y2, the kurtosis coefficient of the response sampled time history, has been com puted by an approximation proposed by Najafian [8], As can be seen in Ref. [8], Eq.…”

Section: Is Tr Ib U Tio N S O F T H E P Ro C E S S P E a K S A mentioning

confidence: 99%

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Conventional and Linear Statistical Moments Applied in Extreme Value Analysis of Non-Gaussian Response of Jack-Ups

Nascimento

Sagrilo²,

Ellwanger³

2015

Journal of Offshore Mechanics and Arctic Engineering

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This work investigates numerically two different methods of moments applied to Hermite derived probability distribution model and variations of Weibull distribution fitted to the short-term time series peaks sample of stochastic response parameters of a simplified jack-up platform model which represents a source of high non-Gaussian responses. The main focus of the work is to compare the results of short-term extreme response statistics obtained by the so-called linear method of moments (L-moments) and the conventional method of moments using either Hermite or Weibull models as the distribution model for the peaks. A simplified mass-spring system representing a three-legged jack-up platform is initially employed in order to observe directly impacts of the linear method of moments (L-moments) in extreme analysis results. Afterward, the stochastic response of the threelegged jack-up platform is analyzed by means of 3D finite element model. Bias and statis tical uncertainty in the estimated extreme statistics parameters are computed considering as the "theoretical" estimates those evaluated by fitting a G umbel to a sample of episodi cal extreme values obtained from distinct short-term realizations (or simulations). Results show that the variability of the extreme results, as a function of the simulation length, determined by the linear method of moments (L-moments) is smaller than their corre sponding ones derived from the conventional method of moments and the biases are more or less the same.

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Section: Derivation Of Distribution Parameters By L-momentsmentioning

confidence: 99%

Section: Is Tr Ib U Tio N S O F T H E P Ro C E S S P E a K S A mentioning

confidence: 99%

Section: Is Tr Ib U Tio N S O F T H E P Ro C E S S P E a K S A mentioning

confidence: 99%

See 1 more Smart Citation

Conventional and Linear Statistical Moments Applied in Extreme Value Analysis of Non-Gaussian Response of Jack-Ups

Nascimento

Sagrilo²,

Ellwanger³

2015

Journal of Offshore Mechanics and Arctic Engineering

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“…Comparison 1 is motivated by the increasing use of L-moments [1] in offshore engineering; e.g., for wave runup [2] and Morison drag [3]. This comparison is made with "Hermite" models, which assume the non-Gaussian response x{t) is a cubic (Hermite) transformation, either to or from a Gaussian process u{t) [4,5].…”

Section: Introductionmentioning

confidence: 99%

Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L-Moments, and Maximum Entropy

Winterstein¹,

MacKenzie

2013

Journal of Offshore Mechanics and Arctic Engineering

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Wind and wave loads on offshore structures show nonlinear effects, which require nonGaussian statistical models. Here we critically review the behavior of various nonGaussian models. We first survey moment-based models; in particular, the four-moment "Hermite" model, a cubic transformation often used in wind and wave applications. We then derive an "L-Hermite" model, an alternative cubic transformation calibrated by the response "L-moments" rather than its ordinary statistical moments. These L-moments have recently found increasing use, in part because they show less sensitivity to distribution tails than ordinary moments. We find here, however, that these L-moments may not convey sufficient information to accurately estimate extreme response statistics. Finally, we show that four-moment maximum entropy models, also applied in the literature, may be inappropriate to model broader-than-Gaussian cases (e.g., responses to wind and wave loads).

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“…The accuracy of the three-parameter distribution model for describing the run-up measurements of a compliant platform was validated through a comparison with the experimental data and other theoretical models. Najafian [13] compared three different methods of moments to estimate the parameters of the Pierson-Holmes distribution [14], which was first introduced as a probability model for Morison wave loads of random waves. In most cases, the sampling variability of the parameter values determined from the two alternative methods of moments was much less than that of the conventional method of moments.…”

Section: Introductionmentioning

confidence: 99%

LH-moment estimation for statistical analysis on the wave crest distributions of a deepwater spar platform model test

et al. 2017

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The design of fixed and compliant offshore platforms requires the reliable estimation of extreme values with small probabilities of exceedance based on an appropriate probability distribution. The Weibull distribution is commonly utilised for the statistical analysis of wave crests, including near-field wave run-ups. The parameters are estimated empirically from experimental or onsite measurements. In this paper, the data set of wave crests from a Spar model test was statistically analysed by using the method of LH-moments for parameter estimation of the Weibull distribution. The root-mean-square errors (RMSEs) and the error of LH-kurtosis were used to examine the goodness-of-fit. The results for the first four LH-moments, the estimated parameters, and the probability distributions showed that the level of the LH-moments has a significant influence. At higher levels, the estimation results gave a more focused representation of the upper part of the wave crest distributions, which indicates consistency with the intention of the method of LH-moments. The low tail RMSE values of less than 2.5% demonstrated that a Weibull distribution model estimated by using high-level LH-moments can accurately represent the probability distribution of large extreme wave crests for incident waves, wave run-ups, and moon pool waves. Goodness-of-fit test on the basis of comparison of sampling LH-kurtosis and theoretical LH-kurtosis was recommended as a procedure for selecting an optimum level

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Comparison of three different methods of moments for derivation of probability distribution parameters

Cited by 9 publications

References 27 publications

Conventional and Linear Statistical Moments Applied in Extreme Value Analysis of Non-Gaussian Response of Jack-Ups

Conventional and Linear Statistical Moments Applied in Extreme Value Analysis of Non-Gaussian Response of Jack-Ups

Extremes of Nonlinear Vibration: Comparing Models Based on Moments, L-Moments, and Maximum Entropy

LH-moment estimation for statistical analysis on the wave crest distributions of a deepwater spar platform model test

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