Fractional absolute moments of heavy tailed distributions

被引：13

作者：

Matsui, Muneya ^{[1
]}

Pawlas, Zbynek ^{[2
]}

机构：

[1] Nanzan Univ, Dept Business Adm, Showa Ku, 18 Yamazato Cho, Nagoya, Aichi 4668673, Japan

[2] Charles Univ Prague, Fac Math & Phys, Dept Probabil & Math Stat, Sokolovska 83, Prague 18675 8, Czech Republic

来源：

BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS | 2016年 / 30卷 / 02期

关键词：

Fractional absolute moments; fractional derivatives; heavy tailed distributions; characteristic functions; infinitely divisible distributions; INFINITELY DIVISIBLE DISTRIBUTION; GENERATING FUNCTION; DERIVATIVES; REGRESSION; PREDICTION; BEHAVIOR; LINNIK;

D O I：

10.1214/15-BJPS280

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Several convenient methods for calculation of fractional absolute moments are given with application to heavy tailed distributions. Our main focus is on an infinite variance case with finite mean, that is, we are interested in formulae for E [vertical bar X - mu vertical bar(gamma)] with 1 < gamma < 2 and mu is an element of R. We review techniques of fractional differentiation of Laplace transforms and characteristic functions. Several examples are given with analytical expressions of E [vertical bar X - mu vertical bar gamma]. We also evaluate the fractional moment errors for both prediction and parameter estimation problems.

引用

页码：272 / 298

页数：27

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