scholarly journals Performance-based comparison of regionalization methods to improve the at-site estimates of daily precipitation

2021 ◽  
Author(s):  
Abubakar Haruna ◽  
Juliette Blanchet ◽  
Anne-Catherine Favre
Keyword(s):  
Pareto Distribution ◽  
Daily Precipitation ◽  
Additive Model ◽  
Generalized Pareto Distribution ◽  
Regional Frequency Analysis ◽  
Distribution Model ◽  
Model Parameters ◽  
Generalized Pareto ◽  
Spatial Method ◽  
Homogeneous Regions

Abstract. In this article, we compare the performances of three regionalization approaches in improving the at-site estimates of daily precipitation. The first method is built on the idea of conventional RFA (Regional Frequency Analysis) but is based on a fast algorithm that defines distinct homogeneous regions relying on their upper tail similarity. It uses only the precipitation data at hand without the need for any additional covariate. The second is based on the region-of-influence (ROI) approach in which neighborhoods, containing similar sites, are defined for each station. The third is a spatial method that adopts Generalized Additive Model (GAM) forms for the model parameters. In line with our goal of modeling the whole range of positive precipitation, the chosen marginal distribution model is the Extended Generalized Pareto Distribution (EGPD) on which we apply the three methods. We consider a dense network composed of 1176 daily stations located within Switzerland and in neighboring countries. We compute different criteria to assess the models' performances both in the bulk of the distribution as well as in the upper tail. The results show that all the regional methods offered improved robustness over the local EGPD model. While the GAM method is more robust and reliable in the upper tail, the ROI method is better in the bulk of the distribution.

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

scholarly journals Spatial distribution of extreme precipitation in the Tibetan Plateau and effects of external forcing factors based on Generalized Pareto distribution

2020 ◽  
Author(s):  
Jiajia Gao ◽  
Jun Du ◽  
Xiaoqing Huang
Keyword(s):  
Spatial Distribution ◽  
Extreme Precipitation ◽  
Pareto Distribution ◽  
Daily Precipitation ◽  
Generalized Pareto Distribution ◽  
The Tibetan Plateau ◽  
External Forcing ◽  
Maximum Rainfall ◽  
Flood Season ◽  
Generalized Pareto

Abstract The daily precipitation data of the years 1955–2017 from May to September were retrieved; then a Generalized Pareto Distribution (GPD) and maximum likelihood methods were adopted to understand trends and calculate the reappearance period of heavy precipitation in the Tibetan Plateau (TP). The daily precipitation values at 22 stations in the TP were found to conform to the model, and theoretical and measured frequencies were consistent. According to the spatial distribution of the maximum precipitation value, the extreme values of Shigatse and Lhasa showed large fluctuations, and the probability of record-breaking precipitation events was low. In the western part of Nagqu, the probability of extreme precipitation was relatively low, and that of record-breaking precipitation was relatively high. The peak values of extreme precipitation in the flood season in the TP generally exhibited a decreasing trend from southeast to northwest, and the extreme value of the flood season that reappeared in the southeast region was approximatelytwice that of the northwest region. The maximum rainfall in most areas will exceed 20 mm in the next 5–10 years, and the maximum rainfall in Shigatse will reach 52.7 mm. After 15 years of recurrence in various regions, the peak rainfall in the flood season has become low. Most of the regions in the model have different responses to ENSO and Indian Ocean monsoon indices with external forcing factors.

scholarly journals Marshall-Olkin Generalized Pareto Distribution: Bayesian and Non Bayesian Estimation

2020 ◽  
pp. 21-33 ◽  
Author(s):  
Hanan Haj AHmad ◽  
Ehab Almetwally
Keyword(s):  
Loss Function ◽  
Bayesian Method ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Least Square Method ◽  
Least Square ◽  
Estimation Methods ◽  
Model Parameters ◽  
Type I ◽  
Generalized Pareto

A new generalization of generalized Pareto Distribution is obtained using the generator Marshall-Olkin distribution (1997). The new distribution MOGP is more flexible and can be used to model non-monotonic failure rate functions. MOGP includes six different sub models: Generalized Pareto, Exponential, Uniform, Pareto type I, Marshall-Olkin Pareto and Marshall-Olkin exponential distribution. We consider different estimation procedures for estimating the model parameters, namely: Maximum likelihood estimator, Maximum product spacing, Least square method, weighted least square method and Bayesian Method. The Bayesian Method is considered under quadratic loss function and Linex loss function. Simulation analysis using MCMC technique is performed to compare between the proposed point estimation methods. The usefulness of MOGP is illustrated by means of real data set, which shows that this generalization is better fit than Pareto, GP and MOP distributions.

Characterization of ERA5 daily precipitation using the extended generalized Pareto distribution

2020 ◽  
Author(s):  
Pauline Rivoire ◽  
Olivia Martius ◽  
Philippe Naveau
Keyword(s):  
Confidence Intervals ◽  
Pareto Distribution ◽  
Daily Precipitation ◽  
Generalized Pareto Distribution ◽  
Value Theory ◽  
Cumulative Distribution ◽  
Simultaneous Occurrence ◽  
Lower Tail ◽  
Generalized Pareto ◽  
Return Levels

<p>Both mean and extreme precipitation are highly relevant and a probability distribution that models the entire precipitation distribution therefore provides important information. Very low and extremely high precipitation amounts have traditionally been modeled separately. Gamma distributions are often used to model low and moderate precipitation amounts and extreme value theory allows to model the upper tail of the distribution. However, difficulties arise when making a link between upper and lower tail. One solution is to define a threshold that separates the distribution into extreme and non-extreme values, but the assignment of such a threshold for many locations is not trivial. </p><p>Here we apply the Extended Generalized Pareto Distribution (EGPD) used by Tencaliec & al. 2019. This method overcomes the problem of finding a threshold between upper and lower tails thanks to a transition function (G) that describes the transition between the empirical distribution of precipitation and a Pareto distribution. The transition cumulative distribution function G has to be constrained by the upper tail and lower tail behavior. G can be estimated using Bernstein polynomials.</p><p>EGPD is used here to characterize ERA-5 precipitation. ERA-5 is a new ECMWF climate re-analysis dataset that provides a numerical description of the recent climate by combining a numerical weather model with observations. The data set is global with a spatial resolution of 0.25° and currently covers the period from 1979 to present.</p><p>ERA-5 daily precipitation is compared to EOBS, a gridded dataset spatially interpolated from observations over Europe, and to CMORPH, a satellite-based global precipitation product. Simultaneous occurrence of extreme events is assessed with a hit rate. An intensity comparison is conducted with return levels confidence intervals and a Kullback Leibler divergence test, both derived from the EGPD.</p><p>Overall, extreme event occurrences between ERA5 and EOBS over Europe appear to agree. The presence of overlap between 95% confidence intervals on return levels highly depends on the season and the probability of occurrence.</p>

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