Another look at plotting positions

Harter, H. Leon

doi:10.1080/03610928408828781

Cited by 87 publications

(37 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A popular one is the so-called Gringorten plotting formula [11] which was deemed more appropriate for the Gumbel distribution in a review of the plotting formulas by Cunnane [12]. Another historical review on the plotting positions is given by Harter [13]. A summary of the commonly used plotting formulas is shown in Table 1 and an example illustrating the effect of using different plotting formulas in estimating the 50-year return value of a variable in Fig.…”

Section: The Problem With the Plotting Positionsmentioning

confidence: 98%

See 1 more Smart Citation

Problems in the extreme value analysis

Makkonen

2008

Structural Safety

View full text Add to dashboard Cite

Section: The Problem With the Plotting Positionsmentioning

confidence: 98%

“…(12) underlines that the plotting positions are unique in the sense that P m depends on m and N only. Consequently, the use of such plotting methods that depend on the distribution of the data or on the application of the analysis [8,[11][12][13][25][26][27][28][29][30][31] is incorrect.…”

Section: Missing the Unique Nature Of The Probability Positionsmentioning

confidence: 99%

Problems in the extreme value analysis

Makkonen

2008

Structural Safety

View full text Add to dashboard Cite

“…De nombreuses formules ont été proposées par différents auteurs et de bonnes études de synthèse existent dans la littérature, par exemple CUN-NANE (1978), JI, et al (1984), et HARTER (1984. Ces formules sont cependant assez semblables d'un point de vue pratique, ce qui laisse supposer que des efforts supplémentaires sur ce sujet seraient peu justifiés.…”

Section: -Introductionunclassified

Justification des formules de probabilité empirique basées sur la médiane de la statistique d'ordre

Rosbjerc¹,

Correa²,

Rasmussen³

2005

rseau

View full text Add to dashboard Cite

Au cours de ces dernières années, beaucoup d'efforts ont été consacrés au développement de formules de probabilité empirique (FPE) non biaisées. En raison même de leur définition, les FPE non biaisées sont dépendantes de la distribution parente des échantillons considérés, et une formule doit donc être établie pour chaque distribution. Dans cette étude on passe en revue les différentes approches pour le développement des FPE, et on montre que la FPE basée sur la médiane des statistiques d'ordre peut constituer un compromis acceptable entre les FPE non biaisées (i.e. correspondant à la moyenne des statistiques d'ordre), et les FPE basées sur le mode des statistiques d'ordre. Contrairement à ces dernières, la FPE basée sur la médiane des statistiques d'ordre est indépendante de la distribution parente des échantillons, et peut donc être utilisée de façon standard. Par ailleurs, la FPE basée sur la médiane des statistiques d'ordre est moins biaisée que la FPE de Weibull, qui est également indépendante de la distribution parente des échantillons. Bien qu'il n'existe pas d'expression analytique exacte pour la FPE basée sur la médiane des statistiques d'ordre, BENARD et BOS-LEVENBACH en ont proposé une très bonne approximation, pm= (m - 0.3)/(n + 0.4). Cette formule est aussi connue sous le nom de formule de Chegodayev.Plotting position formulae (PPFs) maintain an important role in engineering practice. In the area of flood frequency analysis they are used to assign exceedance probabilities to observed floods. In the present study we review various principles for the choice of PPFs. These can be divided into three main categories : (1) formulae based on the observed sample frequencies, (2) formulae based on the distribution of sample frequencies, and (3) formulae based on the distribution of order statistics. PPFs in the first two categories are distribution-free, meaning that no assumption needs to be made regarding the form of the parent distribution of events. The Hazen PPF is an example of a formula belonging to the first category.The Weibull PPF, which is probably the most used formula in practice, belongs to the second category. It can be shown that the frequency corresponding to a particular order statistic is beta distributed regardless of the form of the parent distribution. Being equivalent to the expected value in the beta distribution the Weibull plotting position, pm = m/(n + 1), therefore corresponds to the mean value of sample frequencies. In his book on statistical extremes GUMBEL (1958) recommended the Weibull formula, because it fulfils a set of criteria which he found important. Some of these criteria have later been questioned, for instance by CUNNANE (1978). Various studies have demonstrated that the Weibull PPF is significantly biased in the event domain for most common distributions (an exception is the uniform distribution, where the Weibull PPF is the exact unbiased plotting position).In recent years most attention has been paid to PPFs of the third category. CUNNANE (1978) strongly recommended...

show abstract

“…Development of empirical CDFs of data are discussed elsewhere. 17,20,21 Fitting, Evaluating, and Selecting Parametric Probability Distribution Models A probability distribution model typically is represented as a probability density function (PDF) or a CDF for a continuous random variable. The PDF for a continuous random variable indicates the relative likelihood of values.…”

Section: Visualizing Datamentioning

confidence: 99%

Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NO_xEmissions

Frey

Zheng

2002

Journal of the Air & Waste Management Association

View full text Add to dashboard Cite

The quality of stationary source emission factors is typically described using data quality ratings, which provide no quantification of the precision of the emission factor for an average source, nor of the variability from one source to another within a category. Variability refers to actual differences caused by differences in feedstock composition, design, maintenance, and operation. Uncertainty refers to lack of knowledge regarding the true emissions. A general methodology for the quantification of variability and uncertainty in emission factors, activity factors, and emission inventories (EIs) is described, featuring the use of bootstrap simulation and related techniques. The methodology is demonstrated via a case study for a selected example of NO x emissions from coal-fired power plants. A prototype software tool was developed to implement the methodology. The range of interunit variability in selected activity and emission factors was shown to be as much as a factor of 4, and the range of uncertainty in mean emissions is shown to depend on the interunit variability and sample size. The uncertainty in the total inventory of -16 to +19% was attributed primarily to one technology group, suggesting priorities for collecting data and improving the inventory. The implications for decision-making are discussed.

show abstract

Another look at plotting positions

Cited by 87 publications

References 53 publications

Problems in the extreme value analysis

Problems in the extreme value analysis

Justification des formules de probabilité empirique basées sur la médiane de la statistique d'ordre

Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NO_xEmissions

Contact Info

Product

Resources

About

Another look at plotting positions

Cited by 87 publications

References 53 publications

Problems in the extreme value analysis

Problems in the extreme value analysis

Justification des formules de probabilité empirique basées sur la médiane de la statistique d'ordre

Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NOxEmissions

Contact Info

Product

Resources

About

Quantification of Variability and Uncertainty in Air Pollutant Emission Inventories: Method and Case Study for Utility NO_xEmissions