Identifying the distribution of linear combinations of gamma random variables via Stein’s method

2021 ◽  
pp. 1-8
Author(s):  
Dawei Lu ◽  
Jingcai Yang
Keyword(s):  
Random Variables ◽  
Stein’S Method ◽  
Stein's Method ◽  
Linear Combinations

scholarly journals CLT-related large deviation bounds based on Stein's method

2007 ◽  
Vol 39 (3) ◽  
pp. 731-752 ◽  
Author(s):  
Martin Raič
Keyword(s):  
Random Graphs ◽  
Finite Population ◽  
Large Deviation ◽  
Random Variables ◽  
Stein’S Method ◽  
Stein's Method ◽  
Population Statistics ◽  
Sums Of Random Variables ◽  
Dependence Structures

Large deviation estimates are derived for sums of random variables with certain dependence structures, including finite population statistics and random graphs. The argument is based on Stein's method, but with a novel modification of Stein's equation inspired by the Cramér transform.

scholarly journals New error bounds for Laplace approximation via Stein's method

2021 ◽  
Author(s):  
Robert Gaunt
Keyword(s):  
Convergence Rates ◽  
Random Variables ◽  
Laplace Approximation ◽  
Stein’S Method ◽  
Independent Random Variables ◽  
Stein's Method ◽  
Smooth Test ◽  
Stein Equation ◽  
Technical Advances ◽  
Derivatives Of

We use Stein's method to obtain explicit bounds on the rate of convergence for the Laplace approximation of two different sums of independent random variables; one being a random sum of mean zero random variables and the other being a deterministic sum of mean zero random variables in which the normalisation sequence is random. We make technical advances to the framework of Pike and Ren \cite {pike} for Stein's method for Laplace approximation, which allows us to give bounds in the Kolmogorov and Wasserstein metrics. Under the additional assumption of vanishing third moments, we obtain faster convergence rates in smooth test function metrics. As part of the derivation of our bounds for the Laplace approximation for the deterministic sum, we obtain new bounds for the solution, and its first two derivatives, of the Rayleigh Stein equation.

scholarly journals Compound Poisson Approximation for Dissociated Random Variables via Stein's Method

1999 ◽  
Vol 8 (4) ◽  
pp. 335-346 ◽  
Author(s):  
PETER EICHELSBACHER ◽  
MAŁGORZATA ROOS
Keyword(s):  
System Reliability ◽  
Random Variables ◽  
Poisson Approximation ◽  
Stein’S Method ◽  
Stein's Method ◽  
Compound Poisson ◽  
Compound Poisson Approximation ◽  
Stein Equation

In the present paper we consider compound Poisson approximation by Stein's method for dissociated random variables. We present some applications to problems in system reliability. In particular, our examples have the structure of an incomplete U-statistics. We mainly apply techniques from Barbour and Utev, who gave new bounds for the solutions of the Stein equation in compound Poisson approximation in two recent papers.

scholarly journals Cauchy approximation for sums of independent random variables

2003 ◽  
Vol 2003 (17) ◽  
pp. 1055-1066
Author(s):  
K. Neammanee
Keyword(s):  
Random Variables ◽  
Stein’S Method ◽  
Independent Random Variables ◽  
Stein's Method

We use Stein's method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.

scholarly journals On the constant in the nonuniform version of the Berry-Esseen theorem

2005 ◽  
Vol 2005 (12) ◽  
pp. 1951-1967 ◽  
Author(s):  
K. Neammanee
Keyword(s):  
Rate Of Convergence ◽  
Random Variables ◽  
Stein’S Method ◽  
Independent Random Variables ◽  
Stein's Method ◽  
Concentration Inequality

In 2001, Chen and Shao gave the nonuniform estimation of the rate of convergence in Berry-Esseen theorem for independent random variables via Stein-Chen-Shao method. The aim of this paper is to obtain a constant in Chen-Shao theorem, where the random variables are not necessarily identically distributed and the existence of their third moments are not assumed. The bound is given in terms of truncated moments and the constant obtained is21.44for most values. We use a technique called Stein's method, in particular the Chen-Shao concentration inequality.

scholarly journals CLT-related large deviation bounds based on Stein's method

2007 ◽  
Vol 39 (03) ◽  
pp. 731-752 ◽  
Author(s):  
Martin Raič
Keyword(s):  
Random Graphs ◽  
Finite Population ◽  
Large Deviation ◽  
Random Variables ◽  
Stein’S Method ◽  
Stein's Method ◽  
Population Statistics ◽  
Sums Of Random Variables ◽  
Dependence Structures

Large deviation estimates are derived for sums of random variables with certain dependence structures, including finite population statistics and random graphs. The argument is based on Stein's method, but with a novel modification of Stein's equation inspired by the Cramér transform.

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