scholarly journals Supermodular Stochastic Orders and Positive Dependence of Random Vectors

1997 ◽  
Vol 61 (1) ◽  
pp. 86-101 ◽  
Author(s):  
Moshe Shaked ◽  
J.George Shanthikumar
Keyword(s):  
Stochastic Orders ◽  
Random Vectors ◽  
Positive Dependence

Moving-average models with bivariate exponential and geometric distributions

1987 ◽  
Vol 24 (01) ◽  
pp. 48-61
Author(s):  
Naftali A. Langberg ◽  
David S. Stoffer
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Moment Inequalities ◽  
Random Vectors ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Joint Probabilities

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate geometric marginals. The theory of positive dependence is used to show that in various cases the two classes consist of associated random variables. Association is then applied to establish moment inequalities and to obtain approximations to some joint probabilities of the bivariate processes.

scholarly journals Stochastic orderings of multivariate elliptical distributions

2021 ◽  
Vol 58 (2) ◽  
pp. 551-568
Author(s):  
Chuancun Yin
Keyword(s):  
Necessary Conditions ◽  
Stochastic Orders ◽  
Regularity Conditions ◽  
Elliptical Distributions ◽  
Multivariate Normal ◽  
Random Vectors ◽  
Stochastic Orderings ◽  
Sufficient And Necessary Conditions ◽  
New Inequalities ◽  
Unified Method

AbstractFor two n-dimensional elliptical random vectors X and Y, we establish an identity for $\mathbb{E}[f({\bf Y})]- \mathbb{E}[f({\bf X})]$, where $f\,{:}\, \mathbb{R}^n \rightarrow \mathbb{R}$ satisfies some regularity conditions. Using this identity we provide a unified method to derive sufficient and necessary conditions for classifying multivariate elliptical random vectors according to several main integral stochastic orders. As a consequence we obtain new inequalities by applying the method to multivariate elliptical distributions. The results generalize the corresponding ones for multivariate normal random vectors in the literature.

scholarly journals DEPENDENCE, DISPERSIVENESS, AND MULTIVARIATE HAZARD RATE ORDERING

2005 ◽  
Vol 19 (4) ◽  
pp. 427-446 ◽  
Author(s):  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Multivariate Analysis ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Vectors ◽  
Positive Dependence ◽  
Marginal Distributions ◽  
Dispersive Ordering ◽  
Hazard Rate Ordering

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of two upper orthant dispersive ordered random vectors are also dispersive ordered. Examples and applications are given.

scholarly journals Some positive dependence stochastic orders

2006 ◽  
Vol 97 (1) ◽  
pp. 46-78 ◽  
Author(s):  
Antonio Colangelo ◽  
Marco Scarsini ◽  
Moshe Shaked
Keyword(s):  
Stochastic Orders ◽  
Positive Dependence

Moving-average models with bivariate exponential and geometric distributions

1987 ◽  
Vol 24 (1) ◽  
pp. 48-61 ◽  
Author(s):  
Naftali A. Langberg ◽  
David S. Stoffer
Keyword(s):  
Moving Average ◽  
Random Variables ◽  
Moment Inequalities ◽  
Random Vectors ◽  
Positive Dependence ◽  
Associated Random Variables ◽  
Bivariate Exponential ◽  
Moving Average Models ◽  
Joint Probabilities

Two classes of finite and infinite moving-average sequences of bivariate random vectors are considered. The first class has bivariate exponential marginals while the second class has bivariate geometric marginals. The theory of positive dependence is used to show that in various cases the two classes consist of associated random variables. Association is then applied to establish moment inequalities and to obtain approximations to some joint probabilities of the bivariate processes.

scholarly journals Some Resultats on Optimal Allocation of Policy Limits and Deductibles: Mixture Model

2021 ◽  
Vol 2 ◽  
pp. 4
Author(s):  
Bouhadjar Meriem ◽  
Halim Zeghdoudi ◽  
Abdelali Ezzebsa
Keyword(s):  
Mixture Model ◽  
Expected Utility ◽  
Scalar Product ◽  
Optimal Allocation ◽  
Stochastic Orders ◽  
Frequency Effect ◽  
Dependence Structure ◽  
Random Vectors ◽  
Scalar Products

The main purpose of this paper is to introduce and investigate stochastic orders of scalar products of random vectors. We study the problem of finding maximal expected utility for some functional on insurance portfolios involving some additional (independent) randomization. Furthermore, applications in policy limits and deductible are obtained, we consider the scalar product of two random vectors which separates the severity effect and the frequency effect in the study of the optimal allocation of policy limits and deductibles. In that respect, we obtain the ordering of the optimal allocation of policy limits and deductibles when the dependence structure of the losses is unknown. Our application is a further study of [1 − 6].

Stochastic orders and co-risk measures under positive dependence

2018 ◽  
Vol 78 ◽  
pp. 105-113 ◽  
Author(s):  
M.A. Sordo ◽  
A.J. Bello ◽  
A. Suárez-Llorens
Keyword(s):  
Risk Measures ◽  
Stochastic Orders ◽  
Positive Dependence

Monotonicity of Positive Dependence with Time for Stationary Reversible Markov Chains

1995 ◽  
Vol 9 (2) ◽  
pp. 227-237 ◽  
Author(s):  
Taizhong Hu ◽  
Harry Joe
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
Real Line ◽  
Continuous Time ◽  
Marginal Distribution ◽  
Random Vectors ◽  
Positive Dependence ◽  
Reversible Markov Chain ◽  
Reversible Markov Chains

Let (X1, X2) and (Y1, Y2) be bivariate random vectors with a common marginal distribution (X1, X2) is said to be more positively dependent than (Y1, Y2) if E[h(X1)h(X2)] ≥ E[h(Y1)h(Y2)] for all functions h for which the expectations exist. The purpose of this paper is to study the monotonicity of positive dependence with time for a stationary reversible Markov chain [X1]; that is, (Xs, Xl+s) is less positively dependent as t increases. Both discrete and continuous time and both a denumerable set and a subset of the real line for the state space are considered. Some examples are given to show that the assertions established for reversible Markov chains are not true for nonreversible chains.

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