scholarly journals Threshold detection for the generalized Pareto distribution: Review of representative methods and application to the NOAA NCDC daily rainfall database

2016 ◽  
Vol 52 (4) ◽  
pp. 2659-2681 ◽  
Author(s):  
Andreas Langousis ◽  
Antonios Mamalakis ◽  
Michelangelo Puliga ◽  
Roberto Deidda
Keyword(s):  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Threshold Detection ◽  
Generalized Pareto

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution and a simple representation of the rainfall process

2010 ◽  
Vol 7 (4) ◽  
pp. 4957-4994 ◽  
Author(s):  
R. Deidda
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Rainfall Time Series ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Multiple Threshold ◽  
Optimum Threshold

Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which is able to describe zero and non zero values of rainfall time series by assuring a perfect overlapping with the GPD fitted on the exceedances of any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it will only reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest on the exceedances of a wide range of thresholds using again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations.

scholarly journals A multiple threshold method for fitting the generalized Pareto distribution to rainfall time series

2010 ◽  
Vol 14 (12) ◽  
pp. 2559-2575 ◽  
Author(s):  
R. Deidda
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Rainfall Time Series ◽  
Threshold Method ◽  
Generalized Pareto ◽  
Multiple Threshold ◽  
Optimum Threshold

Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which assures a perfect overlapping with the GPD fitted on the exceedances over any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it is expected to reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest by using exceedances over a wide range of thresholds applying again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions and with a significative percentage of heavily quantized data. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations.

Improving daily rainfall extremes simulation using the generalized Pareto distribution: a case study in Western Iran

2022 ◽  
Vol 85 ◽  
pp. 193-204
Author(s):  
N Shahraki ◽  
S Marofi ◽  
S Ghazanfari
Keyword(s):  
Spatial Correlation ◽  
Water Resource ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Information Criterion ◽  
Rainfall Simulation ◽  
Model Order ◽  
Generalized Pareto ◽  
Agricultural Planning

Prediction of the occurrence or non-occurrence of daily rainfall plays a significant role in agricultural planning and water resource management projects. In this study, gamma distribution function (GDF), kernel, and exponential (EXP) distributions were coupled (piecewise) with a generalized Pareto distribution. Thus, the gamma-generalized Pareto (GGP), kernel-generalized Pareto (KGP), and exponential-generalized Pareto (EGP) models were used. The aim of the present study was to introduce new methods to modify the simulated generation of extreme rainfall amounts of rainy seasons based on the preserved spatial correlation. The best approach was identified using the normalized root mean square error (NRMSE) criterion. For this purpose, the 30-yr daily rainfall datasets of 21 synoptic weather stations located in different climates of West Iran were analyzed. The first, second, and third-order Markov chain (MC) models were used to describe rainfall time series frequencies. The best MC model order was detected using the Akaike information criterion and Bayesian information criterion. Based on the best identified MC model order, the best piecewise distribution models, and the Wilks approach, rainfall events were modeled with regard to the spatial correlation among the study stations. The performance of the Wilks approach was verified using the coefficient of determination. The daily rainfall simulation resulted in a good agreement between the observed and the generated rainfall data. Hence, the proposed approach is capable of helping water resource managers in different contexts of agricultural planning.

scholarly journals Bayesian trend analysis for daily rainfall series of Barcelona

2010 ◽  
Vol 26 ◽  
pp. 71-76 ◽  
Author(s):  
M. I. Ortego ◽  
J. Gibergans-Báguena ◽  
R. Tolosana-Delgado ◽  
J. J. Egozcue ◽  
M. C. Llasat
Keyword(s):  
Climate Change ◽  
Climate Change Scenario ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Daily Rainfall ◽  
Change Scenario ◽  
Generalized Pareto ◽  
Abrupt Changes ◽  
Physical Features ◽  
Threshold Approach

Abstract. A Point-Over-Threshold approach using a reparameterization of the Generalized Pareto Distribution (GPD) has been used to assess changes in the daily rainfall Barcelona series (1854–2006). A Bayesian approach, considering the suitable scale and physical features of the phenomenon, has been used to look for these alterations. Two different models have been assessed: existence of abrupt changes in the new GPD parameters due to modifications of the observatory locations and trends in these GPD parameters, pointing to a climate change scenario.

Inference on P(Y

2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew
Keyword(s):  
Maximum Likelihood ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Maximum Likelihood Estimators ◽  
Record Values ◽  
Asymptotic Distributions ◽  
Bayes Estimators ◽  
Generalized Pareto ◽  
Pareto Distributions ◽  
Generalized Pareto Distributions

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

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.

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