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Wiley2014,Fat-Tailed Distributions: Data, Diagnostics and Dependence pdf

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  • TA的每日心情
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    2016-3-19 06:18
  • 签到天数: 18 天

    [LV.4]偶尔看看III

    发表于 2014-11-16 21:50:42 | 显示全部楼层 |阅读模式
    Roger M. Cooke, Daan Nieboer, "Fat-Tailed Distributions: Data, Diagnostics and Dependence"
    2015 | ISBN-10: 1848217927 | 144 pages | PDF | 1 MB
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    This title is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables.Second, it presents a new measure of obesity. The most popular definitions in terms of regular variation and subexponentiality invoke putative properties that hold at infinity, and this complicates any empirical estimate. Each definition captures some but not all of the intuitions associated with tail heaviness. Chapter 5 studies two candidate indices of tail heaviness based on the tendency of the mean excess plot to collapse as data are aggregated. The probability that the largest value is more than twice the second largest has intuitive appeal but its estimator has very poor accuracy. The Obesity index is defined for a positive random variable X as: Ob(X) = P (X1 +X4 > X2 +X3-X1 For empirical distributions, obesity is defined by bootstrapping. This index reasonably captures intuitions of tail heaviness. Among its properties, if α > 1 then Ob(X) Third and most important, we hope to convince the reader that fat tail phenomena pose real problems; they are really out there and they seriously challenge our usual ways of thinking about historical averages, outliers, trends, regression coefficients and confidence bounds among many other things. Data on flood insurance claims, crop loss claims, hospital discharge bills, precipitation and damages and fatalities from natural catastrophes drive this point home. While most fat tailed distributions are "bad," research in fat tails is one distribution whose tail will hopefully get fatter.

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  • TA的每日心情
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    2018-12-16 14:51
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    [LV.7]常住居民III

    发表于 2014-11-18 10:21:51 | 显示全部楼层
    这本书是入门介绍吧
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  • TA的每日心情

    2015-2-28 19:55
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    [LV.5]常住居民I

    发表于 2014-11-18 13:07:29 | 显示全部楼层
    謝謝,
    來參觀參觀
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  • TA的每日心情
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    2016-1-20 22:12
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    [LV.6]常住居民II

    发表于 2015-1-18 07:34:39 | 显示全部楼层
    看看这本书这么样
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  • TA的每日心情
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    2017-12-15 11:07
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    [LV.7]常住居民III

    发表于 2016-1-1 16:40:29 | 显示全部楼层
    谢谢楼主辛苦分享!!
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  • TA的每日心情
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    5 小时前
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    [LV.10]以坛为家III

    发表于 2017-2-3 16:31:29 | 显示全部楼层
    感谢楼主辛苦分享!!
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