New results for tails of probability distributions according to their asymptotic decay

Cadena, Meitner; Kratz, Marie

doi:10.1016/j.spl.2015.10.018

Cited by 8 publications

(4 citation statements)

References 6 publications

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“…Another instance of a tail-ordering functional in the sense of Proposition 4.1 is the M-index as introduced in Cadena and Kratz (2016). If it exists, it is the unique ρ ∈ R such that lim x→∞ F (x) x ρ+ε = 0 and lim x→∞ F (x) x ρ−ε = ∞ for all ε > 0.…”

Section: Index Of Regular Variation / Tail Indexmentioning

confidence: 99%

Why scoring functions cannot assess tail properties

Brehmer¹,

Strokorb²

2019

Electron. J. Statist.

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Motivated by the growing interest in sound forecast evaluation techniques with an emphasis on distribution tails rather than average behaviour, we investigate a fundamental question arising in this context: Can statistical features of distribution tails be elicitable, i.e. be the unique minimizer of an expected score? We demonstrate that expected scores are not suitable to distinguish genuine tail properties in a very strong sense. Specifically, we introduce the class of max-functionals, which contains key characteristics from extreme value theory, for instance the extreme value index. We show that its members fail to be elicitable and that their elicitation complexity is in fact infinite under mild regularity assumptions. Further we prove that, even if the information of a max-functional is reported via the entire distribution function, a proper scoring rule cannot separate max-functional values. These findings highlight the caution needed in forecast evaluation and statistical inference if relevant information is encoded by such functionals.

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Section: Index Of Regular Variation / Tail Indexmentioning

confidence: 99%

Why scoring functions cannot assess tail properties

Brehmer¹,

Strokorb²

2019

Electron. J. Statist.

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“…A way that facilitates such an analysis, is to use the following relationship given in [30] and e.g. [12,13,14,15].…”

Section: The Ebxiid Familymentioning

confidence: 99%

Extensions of the Burr Type XII distribution and Applications

Cadena

2017

Preprint

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The Burr type XII (BXII) distribution has been largely used in different fields due to its great flexibility for fitting data. These applications have typically involved data showing heavy-tailed behaviors. In order to give more flexibility to the BXII distribution, in this paper, modifications to this distribution through the use of parametric functions are introduced. For instance, members of this new family of distributions allow the analysis not only of data containing extreme values as the BXII distribution, but also of light-tailed data. We refer to this new family of distributions as the extended Burr Type XII distribution (EBXIID) family. Statistical properties of members of the EBXIID family are discussed. The maximum likelihood method is proposed for estimating model parameters. The performance of the new family of distributions is studied using simulations. Applications of the new models to real data sets coming from different domains show that models of the EBXIID family are an alternative to other known distributions.

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“…Recently Cadena et al (see [3,4,4,5,6,7,8]) introduced and studied the class of positive and measurable functions with support R + , bounded on finite intervals, such that…”

Section: Introductionmentioning

confidence: 99%

“…

Recently, new classes of positive and measurable functions, M(ρ) and M(±∞), have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al, 2015(Cadena et al, , 2016(Cadena et al, , 2017. Looking for other suitable normalizing functions than logarithm seems quite natural.

…”

mentioning

confidence: 99%

New Results on the Order of Functions at Infinity

Cadena¹,

Kratz²,

Omey³

2017

SSRN Journal

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Recently, new classes of positive and measurable functions, M(ρ) and M(±∞), have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., , 2017. Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is developed in this paper, studying new classes of functions of the type lim x→∞ log U (x)/H(x) = ρ < ∞ for a large class of normalizing functions H. It provides subclasses of M(0) and M(±∞).

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New results for tails of probability distributions according to their asymptotic decay

Cited by 8 publications

References 6 publications

Why scoring functions cannot assess tail properties

Why scoring functions cannot assess tail properties

Extensions of the Burr Type XII distribution and Applications

New Results on the Order of Functions at Infinity

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