Near-exact distributions for positive linear combinations of independent non-central Gamma random variables

2016 ◽  
Author(s):  
Filipe J. Marques ◽  
Carlos A. Coelho
Keyword(s):  
Random Variables ◽  
Linear Combinations ◽  
Exact Distributions

scholarly journals Some inequalities of linear combinations of independent random variables: II

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1776-1789 ◽  
Author(s):  
Xiaoqing Pan ◽  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Linear Combinations

scholarly journals SOME UNIFIED RESULTS ON COMPARING LINEAR COMBINATIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

2012 ◽  
Vol 26 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Random Variables ◽  
Stochastic Orders ◽  
Sufficient Condition ◽  
Linear Combinations

In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].

scholarly journals Cumulants and partition lattices III: Multiply-indexed arrays

1986 ◽  
Vol 40 (2) ◽  
pp. 161-182 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Random Variables ◽  
Unbiased Estimation ◽  
Linear Combinations ◽  
Components Of Variance ◽  
Partition Lattices ◽  
Special Case

AbstractEarlier work of the author exploiting the role of partition lattices and their Mbius functions in the theory of cumulants, k-statistics and their generalisations is extended to multiply-indexed arrays of random variables. The natural generalisations of cumulants and k-statistics to this context are shown to include components of variance and the associated linear combinations of mean-squares which are used to estimate them. Expressions for the generalised cumulants of arrays built up as sums of independent arrays of effects as in anova models are derived in terms of the generalized cumulants of the effects. The special case of degree two, covering the unbiased estimation of components of variance, is discussed in some detail.

scholarly journals Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
K. Müller ◽  
W.-D. Richter
Keyword(s):  
Computer Program ◽  
Order Statistics ◽  
Stock Exchange ◽  
Random Variables ◽  
Integral Representations ◽  
Symmetric Distribution ◽  
Random Vectors ◽  
Dependent Random Variables ◽  
Exact Distributions

AbstractIntegral representations of the exact distributions of order statistics are derived in a geometric way when three or four random variables depend on each other as the components of continuous ln,psymmetrically distributed random vectors do, n ∈ {3,4}, p > 0. Once the representations are implemented in a computer program, it is easy to change the density generator of the ln,p-symmetric distribution with another one for newly evaluating the distribution of interest. For two groups of stock exchange index residuals, maximum distributions are compared under dependence and independence modeling.

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