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 Some Inequalities of Linear Combinations of Independent Random Variables. I.

2011 ◽  
Vol 48 (4) ◽  
pp. 1179-1188 ◽  
Author(s):  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Sufficient Condition ◽  
Linear Combinations ◽  
Heavy Tailed

In this paper we provide some sufficient conditions to stochastically compare linear combinations of independent random variables. The main results extend those given in Proschan (1965), Ma (1998), Zhao et al. (2011), and Yu (2011). In particular, we propose a new sufficient condition to compare the peakedness of linear combinations of independent random variables which may have heavy-tailed properties.

scholarly journals Some Inequalities of Linear Combinations of Independent Random Variables. I.

2011 ◽  
Vol 48 (04) ◽  
pp. 1179-1188 ◽  
Author(s):  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Sufficient Condition ◽  
Linear Combinations ◽  
Heavy Tailed

In this paper we provide some sufficient conditions to stochastically compare linear combinations of independent random variables. The main results extend those given in Proschan (1965), Ma (1998), Zhao et al. (2011), and Yu (2011). In particular, we propose a new sufficient condition to compare the peakedness of linear combinations of independent random variables which may have heavy-tailed properties.

scholarly journals GENERALIZATION OF THE PAIRWISE STOCHASTIC PRECEDENCE ORDER TO THE SEQUENCE OF RANDOM VARIABLES

2020 ◽  
pp. 1-9
Author(s):  
Maxim Finkelstein ◽  
Nil Kamal Hazra
Keyword(s):  
Random Variables ◽  
Stochastic Ordering ◽  
Independent Random Variables ◽  
Stochastic Orders ◽  
Sufficient Condition ◽  
New Approach ◽  
Stochastic Precedence

Abstract We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence (SP) order that is defined for two random variables to the case n > 2. All conventional stochastic orders are transitive, whereas the SP order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.

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 Stochastic orders for a multivariate Pareto distribution

2021 ◽  
Vol 29 (1) ◽  
pp. 53-69
Author(s):  
Luigi-Ionut Catana
Keyword(s):  
Pareto Distribution ◽  
Random Variables ◽  
Stochastic Orders ◽  
Distribution Family ◽  
Theoretical Results

Abstract In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family. Weak multivariate orders are equivalent or imply different stochastic orders between extremal statistics order of two random variables sequences. The random variables in this article are not neccesary independent.

scholarly journals Non-Comparability with respect to the convex transform order with applications

2020 ◽  
Vol 57 (4) ◽  
pp. 1339-1348
Author(s):  
Idir Arab ◽  
Milto Hadjikyriakou ◽  
Paulo Eduardo Oliveira
Keyword(s):  
Random Variables ◽  
Negative Answer ◽  
Stochastic Orders ◽  
Convex Transform Order

AbstractIn the literature of stochastic orders, one rarely finds results characterizing non-comparability of random variables. We prove simple tools implying the non-comparability with respect to the convex transform order. The criteria are used, among other applications, to provide a negative answer for a conjecture about comparability in a much broader scope than its initial statement.

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