On the moment determinacy of the distributions of compound geometric sums

被引：11

作者：

Lin, GD ^{[1
]}

Stoyanov, J

机构：

[1] Acad Sinica, Inst Stat Sci, Taipei 11529, Taiwan

[2] Univ Newcastle Upon Tyne, Sch Math & Stat, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England

来源：

JOURNAL OF APPLIED PROBABILITY | 2002年 / 39卷 / 03期

关键词：

compound geometric sum; moments; determinate and indeterminate moment problems; Carleman criterion; Krein criterion; Lin condition;

D O I：

10.1017/S0021900200021781

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：

We deal with compound geometric sums of independent positive random variables and study the moment problem for the distributions of such sums (the Stieltjes moment problem). We find conditions under which the distributions are uniquely determined by their moments. We also treat related topics, including the Hamburger moment problem involving random variables on the whole real line. Some conjectures are outlined.

引用

页码：545 / 554

页数：10

共 18 条

[11] KALASHNIKOV V., 1997, MATH APPL, V413
[12] Lin GD, 1997, STAT PROBABIL LETT, V35, P85
[13] LIN GD, 2000, SANKHYA A, V62, P267
[14] Milne R. K., 1989, MATH SCI, V14, P120
[15] Criteria for the unique determination of probability distributions by moments[J]. Pakes, AG;Hung, WL;Wu, JW. AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, 2001(01)
[16] THE MOMENT PROBLEM FOR POLYNOMIAL FORMS IN NORMAL RANDOM-VARIABLES[J]. SLUD, EV. ANNALS OF PROBABILITY, 1993(04)
[17] Krein condition in probabilistic moment problems[J]. Stoyanov, J. BERNOULLI, 2000(05)
[18] A NOTE ON PRESERVATION OF SELF-DECOMPOSABILITY UNDER GEOMETRIC COMPOUNDING[J]. SZEKLI, R. STATISTICS & PROBABILITY LETTERS, 1988(04)

← 1 2 →