Confidence Intervals of the Generalized Pareto Distribution Parameters Based on Upper Record Values

2019 ◽  
Vol 35 (4) ◽  
pp. 909-918 ◽  
Author(s):  
Xu Zhao ◽  
Wei-hu Cheng ◽  
Yang Zhang ◽  
Shao-jie Wei ◽  
Zhen-hai Yang
2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew

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


Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 319 ◽  
Author(s):  
Xuehua Hu ◽  
Wenhao Gui

In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.


2010 ◽  
Vol 26 ◽  
pp. 113-117 ◽  
Author(s):  
R. Tolosana-Delgado ◽  
M. I. Ortego ◽  
J. J. Egozcue ◽  
A. Sánchez-Arcilla

Abstract. A reparametrization of the Generalized Pareto Distribution is here proposed. It is suitable to parsimoniously check trend assumptions within a Point-Over-Threshold model of hazardous events. This is based on considerations about the scale of both the excesses of the event magnitudes and the distribution parameters. The usefulness of this approach is illustrated with a data set from two buoys, where hypotheses about the homogeneity of climate conditions and lack of trends are assessed.


2020 ◽  
Author(s):  
Pauline Rivoire ◽  
Olivia Martius ◽  
Philippe Naveau

<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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