On a characterization of right spread order by the increasing convex order

1999 ◽  
Vol 45 (2) ◽  
pp. 103-110 ◽  
Author(s):  
F. Belzunce
Keyword(s):  
Convex Order ◽  
Increasing Convex Order ◽  
Right Spread Order

scholarly journals Stochastic orders and majorization of mean order statistics

2006 ◽  
Vol 43 (03) ◽  
pp. 704-712 ◽  
Author(s):  
Jesús de la Cal ◽  
Javier Cárcamo
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Stochastic Orders ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Finite Dimensional ◽  
Integrable Functions

We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected order statistics. Such a result includes, as particular cases, previous results by Barlow and Proschan and by Alzaid and Proschan, and, in a sense, completes the picture of known results on order statistics. Applications to other stochastic orders are also briefly considered.

FURTHER RESULTS INVOLVING THE MIT ORDER AND THE IMIT CLASS

2005 ◽  
Vol 19 (3) ◽  
pp. 377-395 ◽  
Author(s):  
I. A. Ahmad ◽  
M. Kayid ◽  
F. Pellerey
Keyword(s):  
Reliability Theory ◽  
Convex Order ◽  
Lifetime Distributions ◽  
Increasing Convex Order ◽  
Shock Models ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Time Class ◽  
Right Spread Order ◽  
The Mean

The purpose of this article is to study several preservation properties of the mean inactivity time order under the reliability operations of convolution, mixture, and shock models. In that context, the increasing mean inactivity time class of lifetime distributions is characterized by means of right spread order and increasing convex order. Some applications in reliability theory are described. Finally, a new test of such a class is discussed.

scholarly journals Stochastic orders and majorization of mean order statistics

2006 ◽  
Vol 43 (3) ◽  
pp. 704-712 ◽  
Author(s):  
Jesús de la Cal ◽  
Javier Cárcamo
Keyword(s):  
Order Statistics ◽  
Random Variables ◽  
Stochastic Orders ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Finite Dimensional ◽  
Integrable Functions

We characterize the (continuous) majorization of integrable functions introduced by Hardy, Littlewood, and Pólya in terms of the (discrete) majorization of finite-dimensional vectors, introduced by the same authors. The most interesting version of this result is the characterization of the (increasing) convex order for integrable random variables in terms of majorization of vectors of expected order statistics. Such a result includes, as particular cases, previous results by Barlow and Proschan and by Alzaid and Proschan, and, in a sense, completes the picture of known results on order statistics. Applications to other stochastic orders are also briefly considered.

On stochastic comparisons of k-out-of-n systems with Weibull components

2018 ◽  
Vol 55 (1) ◽  
pp. 216-232 ◽  
Author(s):  
Narayanaswamy Balakrishnan ◽  
Ghobad Barmalzan ◽  
Abedin Haidari
Keyword(s):  
Weibull Model ◽  
Exponential Model ◽  
Parallel System ◽  
Stochastic Orders ◽  
Open Problems ◽  
Increasing Convex Order ◽  
Scale Parameters ◽  
Convex Transform Order ◽  
Right Spread Order ◽  
The Right

Abstract In this paper we prove that a parallel system consisting of Weibull components with different scale parameters ages faster than a parallel system comprising Weibull components with equal scale parameters in the convex transform order when the lifetimes of components of both systems have different shape parameters satisfying some restriction. Moreover, while comparing these two systems, we show that the dispersive and the usual stochastic orders, and the right-spread order and the increasing convex order are equivalent. Further, some of the known results in the literature concerning comparisons of k-out-of-n systems in the exponential model are extended to the Weibull model. We also provide solutions to two open problems mentioned by Balakrishnan and Zhao (2013) and Zhao et al. (2016).

Zonoids, linear dependence, and size-biased distributions on the simplex

2003 ◽  
Vol 35 (04) ◽  
pp. 871-884 ◽  
Author(s):  
Marco Dall'Aglio ◽  
Marco Scarsini
Keyword(s):  
Random Vector ◽  
Linear Dependence ◽  
Copula Model ◽  
Convex Order ◽  
Dimension 2 ◽  
Concordance Order ◽  
Biased Distribution

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.

scholarly journals Stochastic Comparisons of Symmetric Supermodular Functions of Heterogeneous Random Vectors

2013 ◽  
Vol 50 (02) ◽  
pp. 464-474
Author(s):  
Antonio Di Crescenzo ◽  
Esther Frostig ◽  
Franco Pellerey
Keyword(s):  
Queueing Theory ◽  
Queueing Networks ◽  
Random Variables ◽  
Random Vectors ◽  
Convex Order ◽  
Stochastic Comparisons ◽  
Increasing Convex Order ◽  
Supermodular Functions ◽  
Stop Loss ◽  
Series Systems

Consider random vectors formed by a finite number of independent groups of independent and identically distributed random variables, where those of the last group are stochastically smaller than those of the other groups. Conditions are given such that certain functions, defined as suitable means of supermodular functions of the random variables of the vectors, are supermodular or increasing directionally convex. Comparisons based on the increasing convex order of supermodular functions of such random vectors are also investigated. Applications of the above results are then provided in risk theory, queueing theory, and reliability theory, with reference to (i) net stop-loss reinsurance premiums of portfolios from different groups of insureds, (ii) closed cyclic multiclass Gordon-Newell queueing networks, and (iii) reliability of series systems formed by units selected from different batches.

Stochastic comparisons of interfailure times under a relevation replacement policy

2017 ◽  
Vol 54 (1) ◽  
pp. 134-145 ◽  
Author(s):  
Miguel A. Sordo ◽  
Georgios Psarrakos
Keyword(s):  
Stochastic Order ◽  
Replacement Policy ◽  
Convex Order ◽  
Stochastic Comparisons ◽  
Increasing Convex Order ◽  
Failure Times ◽  
Usual Stochastic Order ◽  
Comparison Results ◽  
Excess Wealth Order ◽  
Cumulative Residual

AbstractWe provide some results for the comparison of the failure times and interfailure times of two systems based on a replacement policy proposed by Kapodistria and Psarrakos (2012). In particular, we show that when the first failure times are ordered in terms of the dispersive order (or, the excess wealth order), then the successive interfailure times are ordered in terms of the usual stochastic order (respectively, the increasing convex order). As a consequence, we provide comparison results for the cumulative residual entropies of the systems and their dynamic versions.

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