Exponential and gamma distributions on positive semigroups, with applications to Dirichlet distributions

被引：1

作者：

Siegrist, Kyle ^{[1
]}

机构：

[1] Univ Alabama, Dept Math Sci, Huntsville, AL 35899 USA

来源：

BERNOULLI | 2007年 / 13卷 / 02期

关键词：

Dirichlet distribution; exponential distribution; gamma distribution; partially ordered set; positive semigroup; zeta distribution;

D O I：

10.3150/07-BEJ5126

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：

In this paper, we give new characterizations of exponential distributions on positive semigroups and we study the corresponding gamma distributions that govern semigroup products of independent and identically distributed exponential variables. We apply these results to the positive integers under multiplication to obtain new interpretations of results on Dirichlet distributions.

引用

页码：330 / 345

页数：16

共 14 条

[1]

Azlarov T.A., 1986, CHARACTERIZATION PRO

[2]

Clifford A., 1967, ALGEBRAIC THEORY SEM, V2

[3]

Clifford AH, 1964, The algebraic theory of semigroups, VI

[4]

Feller W., 1971, INTRO PROBABILITY TH

[5]

Gut Allan, 2006, Rev. Roumaine Math. Pures Appl., V51, P205

[6]

Halmos PR, 1974, MEASURE THEORY

[7]

HOGNAS G, 1995, PROBABILITY MEASURES

[8] The Riemann zeta distribution [J].

Lin, GD ;

Hu, CY .

BERNOULLI, 2001, 7 (05) :817-828

[9]

Pitman J., 2006, Combinatorial Stochastic Processes

[10] Relative aging of distributions [J].

Rowell, G ;

Siegrist, K .

PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 1998, 12 (04) :469-478

← 1 2 →