Parameter estimation for generalized Pareto distribution by generalized probability weighted moment-equations

Chen, Haiqing; Cheng, Weihu; Zhao, Jing; Zhao, Xu

doi:10.1080/03610918.2016.1249884

Cited by 9 publications

(10 citation statements)

References 13 publications

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“…From the simulation study, it is apparent that the repeated sampling behavior of the PWM estimator is poor in general and some modification is needed if it is to work in practice (see e.g., Chen et al 2017). The results also indicate the BRI estimator has a similar MSE to the MLE even for moderated sample size, and its sampling distribution is asymptotically Gaussian (Figure 1 and Table 1).…”

Section: Final Remarksmentioning

confidence: 93%

Estimation of the Pareto and related distributions – A reference-intrinsic approach

Sharpe¹,

Juárez

2021

Communications in Statistics - Theory and Methods

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We study two Bayesian (Reference Intrinsic and Jeffreys prior), two frequentist (MLE and PWM) approaches and the nonparametric Hill estimator for the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capital banks subject to Basel II banking regulations must hold. The Reference Intrinsic approach, which is invariant under one-to-one transformations of the data and parameter, performs better when fitting a generalized Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements.

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Section: Final Remarksmentioning

confidence: 93%

Estimation of the Pareto and related distributions – A reference-intrinsic approach

Sharpe¹,

Juárez

2021

Communications in Statistics - Theory and Methods

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“…Another limitation of the presented algorithm is the selection of a suitable POT method, as the estimation of the parameters of the GPD and the selection of the threshold were strongly related to this. To avoid this issue, it was possible to implement some sophisticated parameter estimator that could deal with the optimal threshold selection (e.g., Zhang's method [51], an estimator based on generalized probability weighted moment equations [52], or a method that combines the method of moments and the likelihood moment [53]), but these are outside the scope of this article. Another challenge was how to combine the ESE of unusually low and unusually high increments together, because both could correspond to a novelty in the data.…”

Section: Limitations and Further Challengesmentioning

confidence: 99%

Introduction to Extreme Seeking Entropy

Vrba

Mareš

2020

Entropy

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Recently, the concept of evaluating an unusually large learning effort of an adaptive system to detect novelties in the observed data was introduced. The present paper introduces a new measure of the learning effort of an adaptive system. The proposed method also uses adaptable parameters. Instead of a multi-scale enhanced approach, the generalized Pareto distribution is employed to estimate the probability of unusual updates, as well as for detecting novelties. This measure was successfully tested in various scenarios with (i) synthetic data, (ii) real time series datasets, and multiple adaptive filters and learning algorithms. The results of these experiments are presented.

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“…Recently, Chen et al 42 proposed a wider class of GPWM (called extended version of GPWM) by considering the PWMs in () with g (·) a suitable measurable function and r and s being real values.…”

Section: Estimators Under Studymentioning

confidence: 99%

A new class of estimators for the shape parameter of a Pareto model

Mateus

Caeiro

2020

Comp and Math Methods

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The Pareto model, first used in socioeconomic problems, has successfully been applied in many other areas such as astronomy, biology, bibliometrics, demography, insurance, or risk management. Although there are several variants of this distribution, the current study focuses on the classic Pareto distribution, also known as the Pareto type I distribution. We propose a new class of estimators for the Pareto shape parameter, obtained through a modification of the probability weighted moment method, called the log generalized probability weighted moments method. In addition to the asymptotic distribution, Monte Carlo simulations were performed to analyze the finite sample behavior of the proposed new estimators. A comparison with the most used estimators, such as the moment, the maximum likelihood, the least squares, and the probability weighted moments estimators was also performed. In addition, the estimators were used to construct asymptotic confidence intervals. To illustrate an application of the different estimation methods to a real data set from a clinical trial complete the article. Results indicate an overall good performance of the new proposed class.

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Parameter estimation for generalized Pareto distribution by generalized probability weighted moment-equations

Cited by 9 publications

References 13 publications

Estimation of the Pareto and related distributions – A reference-intrinsic approach

Estimation of the Pareto and related distributions – A reference-intrinsic approach

Introduction to Extreme Seeking Entropy

A new class of estimators for the shape parameter of a Pareto model

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