Estimation of the Weibull tail-coefficient with linear combination of upper order statistics
By Laurent Gardes, Stéphane Girard. 2008
57 citations recorded by the source corpus.
We present a new family of estimators of the Weibull tail-coefficient. The Weibull tail-coefficient is defined as the regular variation coefficient of the inverse failure rate function. Our estimators are based on a linear combination of log-spacings of the upper order statistics. Their asymptotic normality is established and illustrated for two particular cases of estimators in this family. Their finite sample performances are presented on a simulation study.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/1278c321a7ac372420a92cc61fc22bfabae1441f
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In Artificial Intelligence
- Stéphane Girard
- Laurent Gardes
- Armelle Guillou
- Evarist Gin'e
- Hanie Sedghi
- David Mason
- Philip M. Long
In Statistics and Probability
- Stéphane Girard
- Laurent Gardes
- Armelle Guillou
- Gilles Stupfler
- Evarist Gin'e
- Antoine Schorgen
- Yuri Goegebeur
- Richard Nickl
Citations in the corpus
- A moving window approach for nonparametric estimation of the conditional tail index (2008, methodology): “In this latter case, we also refer to [10] for the definition of kernel estimators based on non-increasing and nonnegative functions, and to [21] for a similar work dedicated to Weibull taildistributions.”
- Sub‐Weibull distributions: Generalizing sub‐Gaussian and sub‐Exponential properties to heavier tailed distributions (2019, unknown): “As a consequence, we consider the slope coefficient in the regression of log Y n − i +1 ,n against log log( n/i ), for 1 ≤ i ≤ k , as an estimate of θ . in This estimator was first introduced by Gardes and Girard (2008) the context of Weibull-tail distributions.”
- Weibull tail-distributions revisited: a new look at some tail estimators (2011, background): “2 Examples In view of Proposition 2(i), Gaussian, gamma, Weibull, Benktander II, logistic and extreme-value distributions all verify (A1(0, θ)) since they are examples of Weibull tail-distributions (see [23], Table 1).”