The method of self-determined probability weighted moments revisited

Whalen, Timothy M.; Savage, Gregory T.; Jeong, Garrett D.

doi:10.1016/s0022-1694(02)00174-9

Cited by 23 publications

(9 citation statements)

References 11 publications

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“…[8,11,12,31,[36][37][38]). Recently, attempts have also been made to avoid the use of plotting positions entirely by iteratively computing the probability weighted moments by the assumed distribution itself [33][34][35]. This method, however, requires a strict pre-assumption of the distribution type and thus gives room for the possibility of circular deduction.…”

Section: Illusion Of the Requirement Of A Good Linear Fitmentioning

confidence: 99%

Problems in the extreme value analysis

Makkonen

2008

Structural Safety

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Section: Illusion Of the Requirement Of A Good Linear Fitmentioning

confidence: 99%

Problems in the extreme value analysis

Makkonen

2008

Structural Safety

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“…(3) Haktanir (1996) proposed an algorithm to compute PWMs by the distribution itself without PPF, which is later called SD-PWMs (Haktanir, 1997;Whalen et al, 2002Whalen et al, , 2004. P nex,i was given by the cumulative distribution function of the probability distribution used…”

Section: Probability Weighted Moments (Pwms)mentioning

confidence: 99%

“…Since PWMs were first defined by Greenwood et al (1979), it attracts many researchers from various scientific and engineering fields (Landwher, Matalas and Wallis, 1979;Wallis, 1987, 1997;Pandey, 2000;Rasmussen, 2001;Whalen et al, 2002;Deng and Pandey, 2008, to name only a few). In contrast with ordinary statistical moments, the main advantage of using PWMs is that their higher order values can be accurately estimated from small samples.…”

Section: Introductionmentioning

confidence: 99%

Derivation of sample oriented quantile function using maximum entropy and self‐determined probability weighted moments

Deng¹,

Pandey²

2009

Environmetrics

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SUMMARYThe paper proposes a new distribution free method for deriving the quantile function of a non-negative random variable using the principle of maximum entropy (MaxEnt) subject to constraints in terms of the self-determined probabilityweighted moments estimated from observed sample data. The principle of MaxEnt constrained by probability weighted moments (PWMs) was utilized to estimate the quantile function. For correct estimation of a quantile function, outliers must be rationally considered in the analysis. However, conventional PWM was criticized for assigning non-exceedance probabilities to sample points based on only their rank number in an ordered series rather than the magnitude of the points themselves, hereby being unable to satisfactorily accommodate outlier in a finite sample. The difficulty in obtaining accurate PWM estimates from samples has been the main impediment to the application of the MaxEnt Principle in extreme quantile estimation. This paper is an attempt to circumvent this difficulty by the use of self-determined probability-weighted moments, which are completely decided by the distribution itself and sample data's magnitude. By interpreting the SD-PWM as moment of quantile function, the paper derives a more rigorous quantile function using MaxEnt principle, which is extraordinarily suitable for cases with small samples containing outliers. An efficient algorithm is presented to estimate the unknown parameters of this sample oriented MaxEnt QF. Comparative studies and numerical analysis are performed to assess the accuracy of the proposed QF estimation method.

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“…The domain of operation of PWM is largely extended thereafter, and there are also some modifications of PWM, e.g. Whalen et al [13] In order to develop a unified approach for the use of order statistics for the statistical analysis of univariate probability distributions, Hosking [14] developed a more easily interpreted technique, called L-Moments, which covers the characterization of probability distributions, the summarization of observed data samples, the fitting of probability distributions to data and the testing of hypotheses about distributional form (for more recent works see refs. [15,16]).…”

Section: Introductionmentioning

confidence: 99%

Application of Bayesian approach to hydrological frequency analysis

Liang

et al. 2011

Sci. China Technol. Sci.

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An existing Bayesian flood frequency analysis method is applied to quantile estimation for Pearson type three (P-III) probability distribution. The method couples prior and sample information under the framework of Bayesian formula, and the Markov Chain Monte Carlo (MCMC) sampling approach is used to estimate posterior distributions of parameters. Different from the original sampling algorithm (i.e. the important sampling) used in the existing approach, we use the adaptive metropolis (AM) sampling technique to generate a large number of parameter sets from Bayesian parameter posterior distributions in this paper. Consequently, the sampling distributions for quantiles or the hydrological design values are constructed. The sampling distributions of quantiles are estimated as the Bayesian method can provide not only various kinds of point estimators for quantiles, e.g. the expectation estimator, but also quantitative evaluation on uncertainties of these point estimators. Therefore, the Bayesian method brings more useful information to hydrological frequency analysis. As an example, the flood extreme sample series at a gauge are used to demonstrate the procedure of application. Bayesian theory, hydrological frequency analysis, Markov Chain Monte Carlo, prior distribution, posterior distribution Citation: Liang Z M, Li B Q, Yu Z B, et al. Application of Bayesian approach to hydrological frequency analysis.

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The method of self-determined probability weighted moments revisited

Cited by 23 publications

References 11 publications

Problems in the extreme value analysis

Problems in the extreme value analysis

Derivation of sample oriented quantile function using maximum entropy and self‐determined probability weighted moments

Application of Bayesian approach to hydrological frequency analysis

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