Bias-corrected geometric-type estimators of the tail index

Brito, Margarida; Cavalcante, Laura; Freitas, Ana Cristina Moreira

doi:10.1088/1751-8113/49/21/214003

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…The asymptotic behavior of these quantile estimators was studied and their asymptotic normality was proved (cf. Brito et al (2014), Dekkers et al (1989) and de Haan and Rootzén (1993)). …”

Section: Extreme Value Theorymentioning

confidence: 99%

“…The problem of reducing the bias of these tail index estimators was addressed in Brito et al (2014), where were proposed the following two asymptotic equivalent geometric-type bias corrected estimators…”

Section: Extreme Value Theorymentioning

confidence: 99%

“…Considering the following distributional representation of the geometric-type estimator (see Brito et al (2014), Theorem 2.2. )…”

Section: Estimation Of Tail Parametersmentioning

confidence: 99%

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Modeling of Extremal Earthquakes

Brito

Cavalcante

Freitas

2015

CIM Series in Mathematical Sciences

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Natural hazards, such as big earthquakes, affect the lives of thousands of people at all levels. Extreme-value analysis is an area of statistical analysis particularly concerned with the systematic study of extremes, providing an useful insight to fields where extreme values are probable to occur. The characterization of the extreme seismic activity is a fundamental basis for risk investigation and safety evaluation. Here we study large earthquakes in the scope of the Extreme Value Theory. We focus on the tails of the seismic moment distributions and we propose to estimate relevant parameters, like the tail index and high order quantiles using the geometric-type estimators.In this work we combine two approaches, namely an exploratory oriented analysis and an inferential study. The validity of the assumptions required are verified, and both geometric-type and Hill estimators are applied for the tail index and quantile estimation. A comparison between the estimators is performed, and their application to the considered problem is illustrated and discussed in the corresponding context.

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“…The asymptotic behavior of these quantile estimators was studied and their asymptotic normality was proved (cf. Brito et al (2014), Dekkers et al (1989) and de Haan and Rootzén (1993)). …”

Section: Extreme Value Theorymentioning

confidence: 99%

Section: Extreme Value Theorymentioning

confidence: 99%