Statistical Methods in Hydrology

Beard, Leo R.

doi:10.21236/ada052593

Cited by 70 publications

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“…La préférence pour la valeur la plus probable (ou valeur modale) a aussi été critiquée par BEARD (1943), qui soutient que même si le mode est plus probable que la moyenne ou la médiane, la probabilité de l'obtenir demeure infinitésimale. Il a préféré la médiane à la moyenne et au mode parce qu'elle conduit à des probabilités empiriques basées sur les statistiques d'ordre et indépendantes de la distribution parente.…”

Section: -Discussionunclassified

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

Rosbjerc¹,

Correa²,

Rasmussen³

2005

rseau

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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...

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Section: -Discussionunclassified

“…BEARD (1943) a quant à lui choisi la médiane p 1 comme FPE de la plus grande valeur observée. Malheureusement il n'existe pas de formule explicite donnant la médiane d'une distribution bêta en général, BEARD (1943) a proposé la FPE approximative suivante :…”

Section: -F (Xf) F (X) Is the Cumulative Distribution Function To Beunclassified

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

Rosbjerc¹,

Correa²,

Rasmussen³

2005

rseau

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“…This formula was proposed by Beard (1943) and presented in detail by Jenkinson (1977). It is proved by Folland and Anderson (2002) that this method performed as well as other empirical ranking formulas.…”

Section: Methods Description 321 Jenkinson Empirical Ranking Formulamentioning

confidence: 99%

“…As an identical classification of extremes is not comparable among the areas with greatly varying climates, empirical ranking methods are recommended to determine the extreme threshold at different percentiles. Therefore, the formula introduced by Beard (1943) has come into wide use because it is more suitable for studies on the changing climate extremes (Folland and Anderson, 2002).…”

Section: Introductionmentioning

confidence: 99%

Climatological features and trends of extreme precipitation during 1979–2012 in Beijing, China

Chu

2015

Proc. IAHS

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Abstract. In this study, three kinds of hourly precipitation series with the spatial resolution of 0.1 • are used to analyze the climatological features and trends of extreme precipitation during the period of 1979-2012 in Beijing, China. The results show that: (1) the spatial distribution of median annual precipitation, with a range from 500 to 825 mm, is similar to that of local topography, which increases from the northwest to the southeast. Taking the urban area as a centre, the inter-annual precipitation in the Beijing area displays an outward decreasing tendency at the maximum rate of 125 mm per decade (125 mm × 10 a −1 ); (2) extreme precipitation amount, which accounts for 40-48 % of total precipitation amount, has a similar spatial distribution to average annual precipitation; (3) the spatial distribution of extreme precipitation days and threshold estimated as the upper 95 percentile are significantly different from that of extreme precipitation, with maximum values concentrated on the urban area and the eastern mountain area, and minimum values in northwest; (4) extreme precipitation days (Ex_pd95) show an opposite distribution to extreme precipitation threshold (Ex_pv95), indicating that areas with greater precipitation threshold may has less precipitation days, and vice versa; (5) an apparent spatiotemporal decreasing tendency is detected in extreme precipitation amount. The downward tendencies are also found in extreme precipitation threshold. Unlike Ex_pv95, in most of the study area, Ex_pd95 is virtually unchanged; (6) downward trends of extreme precipitation is slightly smaller than that of annual precipitation, and the reducing amplitude of north-eastern areas are much higher than the areas in the southwest.

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“…이러한 확률도시위치를 결정하는 도시위치공식은 1914 년에 Hazen이 제안한 이후 꾸준히 연구되어 왔다 (Weibull, 1939;Beard, 1942;Kimball, 1946;Blom, 1958;Gumbel, 1958;Kimball, 1960;Gringorten, 1963;Filliben, 1969;Benson, 1975;Cunnane, 1978;Adamowski, 1981;Xuewu et al, 1984;Arnell et al, 1986;Nguyen et al, 1989;Guo, 1990b;Nguyen and In-na, 1992;Goel and De, 1993;Haktanir and Bozduman, 1995;De, 2000;김수영 등, 2009). Kimball(1946)은 표본자료의 순서통계량(order statistics) 에 대한 기대값 형태로 나타나는 평균 개념을 적용한 도 시위치를 제안하였으며, Blom(1958) 은 Kimball (1946)이 제안한 개념을 보다 범용적으로 적용할 수 있는       의 관계를 제안한 바 있다.…”

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Derivation of Plotting Position Formulas Considering the Coefficients of Skewness for the GEV Distribution

Kim¹,

Heo²,

Choi³

2011

Journal of Korea Water Resources Association

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Probability plotting position is generally used for the graphical analysis of the annual maximum quantile and the estimation of exceedance probability to display the fitness between sample and an appropriate probability distribution. In addition, it is used to apply a specific goodness of fit test. Plotting position formula to define the probability plotting position has been studied in many researches. Especially, the GEV distribution which is an important probability distribution to analyze the frequency of hydrologic data was popular. In this study, the theoretical reduced variates are derived using the mean value of order statistics to derived an appropriate plotting position formula for the GEV distribution. In addition, various forms of plotting position formula considering various sample sizes and coefficients of skewness related with shape parameters are applied. The parameters of plotting position formulas are estimated using the genetic algorithm. The accuracy of derived plotting position formula is estimated by the errors between the theoretical reduced variates and those by various plotting position formulas including the derived ones in this study. As a result, the errors by derived plotting position formula is the smallest at the range of shape parameter with -0.25～0.10.

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Statistical Methods in Hydrology

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Cited by 70 publications

References 0 publications

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

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

Climatological features and trends of extreme precipitation during 1979–2012 in Beijing, China

Derivation of Plotting Position Formulas Considering the Coefficients of Skewness for the GEV Distribution

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