On Approximating the Distribution of Quadratic Forms in Gamma Random Variables and Exponential Order Statistics

被引：0

作者：

A. Akbar Mohsenipour

Serge B. Provost

机构：

[1] The University of Western Ontario London,Department of Statistical and Actuarial Sciences

来源：

Journal of Statistical Theory and Applications | 2013年 / 12卷 / 2期

关键词：

Quadratic forms; Exponential random variables; Order statistics; Generalized gamma distribution; Moments; Density approximation;

D O I：

10.2991/jsta.2013.12.2.4

中图分类号：

学科分类号：

摘要：

This paper proposes a moment-based approximation to the distribution of quadratic forms in gamma random variables. Quadratic forms in order statistics from an exponential population are considered as well. Actually, several test statistics can be expressed in terms of the latter. The density approximants are expressible as the product of a gamma type distributed base density function and a polynomial adjustment. Several illustrative examples are provided.

引用

页码：173 / 184

页数：11

共 16 条

[1]

del Barrio E(2005)Asymptotics for Bernoulli 11 131-189

[2]

Giné E(2002) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances Journal of Econometrics 109 305-340

[3]

Utzet F(1972)Superconsistent estimation and inference in structural econometric models using extreme order statistics Biometrika 59 605-611

[4]

Donald SG(1985)Quadratic forms in order statistics used as goodness-of-fit criteria Canad. J. Statist 13 253-256

[5]

Paarsch HJ(1987)The asymptotic distribution of the correlation coefficient in testing fit to the exponential distribution Canad. J. Statist 15 159-167

[6]

Hartley HO(2010)On the asymptotic efficiency of correlation tests of fit Journal of Statistical Research 44 315-334

[7]

Pfaffenberger RC(2012)On approximating the distributions of ratios and differences of noncentral quadratic forms in normal vectors Journal of the Iranian Statistical Society 11 147-171

[8]

Lockhart RA(2005)Approximating the distributions of singular quadratic expressions and their ratios The Mathematica Journal 9 727-756

[9]

McLaren CG(1995)Moment-based density approximants The American Statistician 49 217-219

[10]

Lockhart RA(undefined)A recursive formulation of the old problem of obtaining moments from cumulants and vice versa undefined undefined undefined-undefined

← 1 2 →