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

共 50 条

[21] On learning mixtures of heavy-tailed distributions
Dasgupta, A
Hopcroft, J
Kleinberg, J
Sandler, M
46th Annual IEEE Symposium on Foundations of Computer Science, Proceedings, 2005, : 491 - 500
[22] On the emergence of heavy-tailed streamflow distributions
Basso, S.
Schirmer, M.
Botter, G.
ADVANCES IN WATER RESOURCES, 2015, 82 : 98 - 105
[23] A PARAMETRIC BOOTSTRAP FOR HEAVY-TAILED DISTRIBUTIONS
Cornea-Madeira, Adriana
Davidson, Russell
ECONOMETRIC THEORY, 2015, 31 (03) : 449 - 470
[24] DESCRIBING AND TESTING FOR HEAVY-TAILED DISTRIBUTIONS
BRYSON, MC
BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY, 1973, 54 (03) : 272 - 272
[25] Heavy-tailed distributions in combinatorial search
Gomes, CP
Selman, B
Crato, N
PRINCIPLES AND PRACTICE OF CONSTRAINT PROGRAMMING - CP 97, 1997, 1330 : 121 - 135
[26] HEAVY-TAILED DISTRIBUTIONS - PROPERTIES AND TESTS
BRYSON, MC
TECHNOMETRICS, 1974, 16 (01) : 61 - 68
[27] Appendix: A primer on heavy-tailed distributions
Karl Sigman
Queueing Systems, 1999, 33 : 261 - 275
[28] Structural equation modeling with heavy tailed distributions
Yuan, KH
Bentler, PM
Chan, W
PSYCHOMETRIKA, 2004, 69 (03) : 421 - 436
[29] Heavy-tailed fractional Pearson diffusions
Leonenko, N. N.
Papic, I.
Sikorskii, A.
Suvak, N.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2017, 127 (11) : 3512 - 3535
[30] On the proximity of distributions in terms of coinciding fractional moments
Tagliani, A
APPLIED MATHEMATICS AND COMPUTATION, 2003, 145 (2-3) : 501 - 509

← 1 2 3 4 5 →