Stein characterizations for linear combinations of gamma random variables

Some Unified Results on Comparing Linear Combinations of Independent Gamma Random Variables

Assessing stochastic algorithms for large scale nonlinear least squares problems using extremal probabilities of linear combinations of gamma random variables

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where the uncertainties in the major stochastic steps are quantified. Such stochastic steps involve approximating the NLS objective function using Monte-Carlo meth...

On the Linear Combination of Exponential and Gamma Random Variables

The exact distribution of the linear combination αX + βY is derived when X and Y are exponential and gamma random variables distributed independently of each other. A measure of entropy of the linear combination is investigated. We also provide computer programs for generating tabulations of the percentage points associated with the linear combination. The work is motivated by examples in autom...

The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables

In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...

Laws of Large Numbers for Random Linear

The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...