Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation

Gorshenin, Andrey; Korolev, V. Yu.

doi:10.1007/s10958-018-4052-1

Cited by 6 publications

(15 citation statements)

References 12 publications

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“…The function (3) is a scale mixture of the Fréchet (inverse Weibull) distribution. It can be demonstrated [4]…”

Section: The Tempered Snedecor-fisher Distribution As An Asymptotic Amentioning

confidence: 98%

“…As it has been demonstrated in [4,11], the asymptotic probability distribution of extremal daily precipitation within a wet period can be represented as follows (here r > 0, λ > 0, and γ > 0):…”

Section: The Tempered Snedecor-fisher Distribution As An Asymptotic Amentioning

confidence: 99%

“…Some properties of the distribution of the r.v. M r,γ,λ were discussed in [4]. In particular, it was shown that the limit distribution (3) can be represented as a scale mixture of exponential or stable or Weibull or Pareto or folded normal laws (r ∈ (0, 1], γ ∈ (0, 1], λ > 0):…”

Section: The Tempered Snedecor-fisher Distribution As An Asymptotic Amentioning

confidence: 99%

“…Fisher distribution model to real data Some methods of statistical estimation of the parameters r, λ and γ of the tempered Snedecor-Fisher distribution (3) were described in [4]. In this section the algorithms and corresponding formulas for practical computation are briefly given.…”

Section: The Algorithms Of Statistical Fitting Of the Tempered Snedecor-mentioning

confidence: 99%

“…The fitted Pareto model for the daily precipitation volume [4] together with the observation that the duration of a wet period has the negative binomial distribution makes it possible to propose a reasonable model for the distribution of the maximum daily precipitation within a wet period as an asymptotic approximation provided by the limit theorems for extreme order statistics in samples with random size. We will give a strict derivation of such a model having the form of the tempered Snedecor-Fisher distribution (that is, the distribution of a positive power of a random variable with the Snedecor-Fisher distribution) and discuss its properties as well as some methods of statistical estimation of its parameters.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Tests for Extreme Precipitation Volumes

2019

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The approaches, based on the negative binomial model for the distribution of duration of the wet periods measured in days, are proposed to the definition of extreme precipitation. This model demonstrates excellent fit with real data and provides a theoretical base for the determination of asymptotic approximations to the distributions of the maximum daily precipitation volume within a wet period as well as the total precipitation volume over a wet period. The first approach to the definition (and determination) of extreme precipitation is based on the tempered Snedecor-Fisher distribution of the maximum daily precipitation. According to this approach, a daily precipitation volume is considered to be extreme, if it exceeds a certain (pre-defined) quantile of the tempered Snedecor-Fisher distribution. The second approach is based on that the total precipitation volume for a wet period has the gamma distribution. Hence, the hypothesis that the total precipitation volume during a certain wet period is extremely large can be formulated as the homogeneity hypothesis of a sample from the gamma distribution. Two equivalent tests are proposed for testing this hypothesis. Both of these tests deal with the relative contribution of the total precipitation volume for a wet period to the considered set (sample) of successive wet periods. Within the second approach it is possible to introduce the notions of relatively and absolutely extreme precipitation volumes. The results of the application of these tests to real data are presented yielding the conclusion that the intensity of wet periods with extreme large precipitation volume increases.

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“…The function (3) is a scale mixture of the Fréchet (inverse Weibull) distribution. It can be demonstrated [4]…”

Section: The Tempered Snedecor-fisher Distribution As An Asymptotic Amentioning

confidence: 98%

Section: The Tempered Snedecor-fisher Distribution As An Asymptotic Amentioning

confidence: 99%

Section: The Tempered Snedecor-fisher Distribution As An Asymptotic Amentioning

confidence: 99%

Section: The Algorithms Of Statistical Fitting Of the Tempered Snedecor-mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical Tests for Extreme Precipitation Volumes

2019

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Max-Compound Cox Processes. I

2019

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Genome-wide association study of a semicontinuous trait: illustration of the impact of the modeling strategy through the study of Neutrophil Extracellular Traps levels

Munsch

Proust

Labrouche-Colomer

et al. 2023

NAR Genomics and Bioinformatics

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Over the last years, there has been a considerable expansion of genome-wide association studies (GWAS) for discovering biological pathways underlying pathological conditions or disease biomarkers. These GWAS are often limited to binary or quantitative traits analyzed through linear or logistic models, respectively. In some situations, the distribution of the outcome may require more complex modeling, such as when the outcome exhibits a semicontinuous distribution characterized by an excess of zero values followed by a non-negative and right-skewed distribution. We here investigate three different modeling for semicontinuous data: Tobit, Negative Binomial and Compound Poisson-Gamma. Using both simulated data and a real GWAS on Neutrophil Extracellular Traps (NETs), an emerging biomarker in immuno-thrombosis, we demonstrate that Compound Poisson-Gamma was the most robust model with respect to low allele frequencies and outliers. This model further identified the MIR155HG locus as significantly (P = 1.4 × 10−8) associated with NETs plasma levels in a sample of 657 participants, a locus recently highlighted to be involved in NETs formation in mice. This work highlights the importance of the modeling strategy for GWAS of a semicontinuous outcome and suggests Compound Poisson-Gamma as an elegant but neglected alternative to Negative Binomial for modeling semicontinuous outcome in the context of genomic investigations.

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Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation

Cited by 6 publications

References 12 publications

Statistical Tests for Extreme Precipitation Volumes

Statistical Tests for Extreme Precipitation Volumes

Max-Compound Cox Processes. I

Genome-wide association study of a semicontinuous trait: illustration of the impact of the modeling strategy through the study of Neutrophil Extracellular Traps levels

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