# Statistics of extremes

##### Citations

615 citations

572 citations

### Cites background from "Statistics of extremes"

...Davison and Gholamrezaee (2012) fit models based on (22) and (23) to extreme temperature data....

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...Padoan, Ribatet and Sisson (2010), Blanchet and Davison (2011) and Davison and Gholamrezaee (2012) discuss its application in the context of extremal inference, and its use to fit spatial extremal models based on (21) and (22) has been implemented in the R libraries SpatialExtremes and CompRandFld....

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361 citations

291 citations

### Cites background from "Statistics of extremes"

...equivalently, that the underlying distribution is the Gumbel. It is highly probable for a null hypothesis with small values of , e.g., H0: 1⁄4 0.01 or H0: 1⁄4 0.01 not to be rejected. Hence, we deem that it is not possible to conclude with certainty applying statistical tests whether the underlying distribution is Gumbel or GEV with close to zero. [29] Nevertheless, apart from the aforementioned tests, graphical tools exist that are especially useful when dealing with a large number of records, which can help to make inference about the underlying distribution. A graphical tool that has gained popularity over the last decade, introduced by Hosking [1990], is provided by the L-moments ratio diagrams....

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...…has been an active research field and a matter of debate for more than half a century dating back to the works of E. J. Gumbel in 1940s; however, the field of extreme value theory seems to have originated more than three centuries ago in the works of Nicolaus Bernoulli [see e.g., Gumbel, 1958]....

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261 citations

##### References

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3,060 citations

### "Statistics of extremes" refers background in this paper

...This approach is equivalent to attributing an approximate exponential distribution with mean ξ to large log Yj , and it yields the celebrated Hill (1975) estimator ξ̂H,k = k−1 k∑ j=1 log[Y (n+1− j )/Y (n−k)], (29) where Y (1) ≤ · · · ≤ Y (n) denote the ordered Yj ....

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2,037 citations

### "Statistics of extremes" refers background in this paper

...The identification of limiting distributions for maxima is attributable to Fisher & Tippett (1928), whose work was further developed by von Mises (1936), Gnedenko (1943), and many others....

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...This question was addressed by von Mises (1936) and particularly by Gnedenko (1943), who provided necessary and sufficient conditions for F ∈ MDAξ in terms of the upper tail properties of F (de Haan & Ferreira 2006, chapter 1)....

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1,503 citations

1,275 citations