Distribution of a sum of weighted central Chi-square variables

被引：40

作者：

Castaño-Martínez, A

López-Blázquez, F

机构：

[1] Univ Cadiz, Dept Estadist & Invest Operat, Cadiz, Spain

[2] Univ Sevilla, Dept Estadist & Invest Operat, Seville, Spain

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2005年 / 34卷 / 03期

关键词：

gamma distribution; inverse Laplace transform; Laguerre expansion; truncation error; unbiased estimation;

D O I：

10.1081/STA-200052148

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 derive a Laguerre expansion for the inverse Laplace transform, based on the estimation problem in the gamma distribution. This procedure is used to obtain the density and distribution functions of a sum of positive weighted central chi-square variables as a series in Laguerre polynomials. The formulas so obtained will depend on certain parameters which adequately chosen will give some expressions already known in the literature and some new ones. Finally, we obtain bounds for the truncation error in the numerical approximations.

引用

页码：515 / 524

页数：10

共 22 条

[1] CONSTRUCTION OF UNIFORMLY MINIMUM VARIANCE UNBIASED ESTIMATORS FOR EXPONENTIAL DISTRIBUTIONS [J].