Single station and regional analysis of daily rainfall extremes

Fitzgerald, D. L.

doi:10.1007/bf01543461

Cited by 40 publications

(16 citation statements)

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“…This model has been further developed by Madsen et al [1994Madsen et al [ , 1995, who assumed generalized Pareto (GP) distributed exceedances and applied the model in a regional analysis of extreme precipitation. Fitzgerald [1989] also considered the GP distribution and proposed a method where the shape parameter is inferred from regional data.…”

Section: Introductionmentioning

confidence: 99%

The partial duration series method in regional index‐flood modeling

Madsen¹,

Rosbjerg²

1997

Water Resources Research

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Abstract. A regional index-flood method based on the partial duration series model is introduced. The model comprises the assumptions of a Poisson-distributed number of threshold exceedances and generalized Pareto (GP) distributed peak magnitudes. The regional T-year event estimator is based on a regional estimate of the GP shape parameter. Analytical approximations of bias and variance of the regional T-year event estimator are deduced. The performance of the regional method is evaluated in the case of regional heterogeneity and intersite dependence. For small to moderate sample sizes, the regional estimator is superior to the at-site estimator even in extremely heterogenous regions, the performance of the regional estimator being relatively better in regions with a negative shape parameter. When the record length increases, the relative performance of the regional estimator decreases, but it is still preferable to at-site estimation in moderately heterogeneous and homogeneous regions for large sample sizes. Modest intersite dependence has only a small effect on the performance of the regional indexflood estimator.

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Section: Introductionmentioning

confidence: 99%

The partial duration series method in regional index‐flood modeling

Madsen¹,

Rosbjerg²

1997

Water Resources Research

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“…While Van Montfort and Witter [1986] used maximum likelihood estimation, Fitzgerald [1989] chose the probability-weighted moments (PWM) for estimation of the GPD parameters as proposed by Hosking and Wallis [1987]. Here the performance of the PWM estimator of the T-year event will be compared to the classical method of moments (MOM) estimator.…”

Section: Introductionmentioning

confidence: 99%

Prediction in partial duration series with generalized pareto‐distributed exceedances

Rosbjerg¹,

Madsen²,

Rasmussen³

1992

Water Resources Research

145

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As a generalization of the common assumption of exponential distribution of the exceedances in partial duration series the generalized Pareto distribution has been adopted. Estimators for the parameters are presented using estimation by both method of moments and probability‐weighted moments. The corresponding estimators for the T‐year event are given and approximate expressions for bias and variance of the estimators are derived in both cases. Using the mean square error of the T‐year event estimator as a performance index it is shown that the method of moments is preferable to the probability‐weighted moments. Maintaining the generalized Pareto distribution as the parent exceedance distribution the T‐year event is estimated assuming the exceedances to be exponentially distributed. For moderately long‐tailed exceedance distributions and small to moderate sample sizes it is found, by comparing mean square errors of the T‐year event estimators, that the exponential distribution is preferable to the correct generalized Pareto distribution despite the introduced model error and despite a possible rejection of the exponential hypothesis by a test of significance. For moderately short‐tailed exceedance distributions (with physically justified upper limit) the correct exceedance distribution should be applied despite a possible acceptance of the exponential assumption by a test of significance.

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“…Exceedance theory spreads, originating mainly from hydrological literature (see e.g. Balkema & De Hahn 1974; Fitzgerald 1989), into many fields of applied statistics. The basic notion is that, instead of studying the distribution of the maxima in blocks of random variables as in , an alternative view is to consider realizations X i drawn from an underlying distribution F as extreme, if they exceed a very high threshold t as depicted in Fig.…”

Section: Extreme Value Statisticsmentioning

confidence: 99%

On the modelling of the excesses of galaxy clusters over high-mass thresholds

Waizmann¹,

Ettori²,

Moscardini³

2012

Monthly Notices of the Royal Astronomical Society

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In this work we present for the first time an application of the Pareto approach to the modelling of the excesses of galaxy clusters over high‐mass thresholds. The distribution of those excesses can be described by the generalized Pareto distribution (GPD), which is closely related to the generalized extreme value (GEV) distribution. After introducing the formalism, we study the impact of different thresholds and redshift ranges on the distributions, as well as the influence of the survey area on the mean excess above a given mass threshold. We also show that both the GPD and GEV approaches lead to identical results for rare, thus high‐mass and high‐redshift, clusters. As an example, we apply the Pareto approach to ACT‐CL J0102−4915 and SPT‐CL J2106−5844 and derive the respective cumulative distribution functions of the exceedance over different mass thresholds. We also study the possibility to use the GPD as a cosmological probe. Since in the maximum likelihood estimation of the distribution parameters all the information from clusters above the mass threshold is used, the GPD might offer an interesting alternative to GEV‐based methods that use only the maxima in patches. When comparing the accuracy with which the parameters can be estimated, it turns out that the patch‐based modelling of maxima is superior to the Pareto approach. In an ideal case, the GEV approach is capable to estimate the location parameter with a per cent level precision for less than ∼100 patches. This result makes the GEV‐based approach potentially also interesting for cluster surveys with a smaller area.

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Single station and regional analysis of daily rainfall extremes

Cited by 40 publications

References 1 publication

The partial duration series method in regional index‐flood modeling

The partial duration series method in regional index‐flood modeling

Prediction in partial duration series with generalized pareto‐distributed exceedances

On the modelling of the excesses of galaxy clusters over high-mass thresholds

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