Testing for increasing convex order in several populations

2003 ◽  
Vol 55 (1) ◽  
pp. 121-136 ◽  
Author(s):  
Xinsheng Liu ◽  
Jinde Wang
Keyword(s):  
Convex Order ◽  
Increasing Convex Order

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.

scholarly journals Positive Dependence of Signals

2010 ◽  
Vol 47 (3) ◽  
pp. 893-897 ◽  
Author(s):  
Michel Denuit
Keyword(s):  
Conditional Expectation ◽  
Conditional Variance ◽  
Sufficient Condition ◽  
Convex Order ◽  
Positive Dependence ◽  
Increasing Convex Order ◽  
Quantity Of Interest ◽  
Conditional Expectations ◽  
Special Case

In this paper we further investigate the problem considered by Mizuno (2006) in the special case of identically distributed signals. Specifically, we first propose an alternative sufficient condition of crossing type for the convex order to hold between the conditional expectations given signal. Then, we prove that the bivariate (2,1)-increasing convex order ensures that the conditional expectations are ordered in the convex sense. Finally, the L2 distance between the quantity of interest and its conditional expectation given signal (or expected conditional variance) is shown to decrease when the strength of the dependence increases (as measured by the (2,1)-increasing convex order).

Increasing convex order on generalized aggregation of SAI random variables with applications

2017 ◽  
Vol 54 (3) ◽  
pp. 685-700 ◽  
Author(s):  
Xiaoqing Pan ◽  
Xiaohu Li
Keyword(s):  
Linear Combination ◽  
Kernel Function ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Special Cases ◽  
Arrangement Increasing

Abstract In this paper we study general aggregation of stochastic arrangement increasing random variables, including both the generalized linear combination and the standard aggregation as special cases. In terms of monotonicity, supermodularity, and convexity of the kernel function, we develop several sufficient conditions for the increasing convex order on the generalized aggregations. Some applications in reliability and risks are also presented.

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.

A NOTE ON BOUNDS AND MONOTONICITY OF SPATIAL STATIONARY COX SHOT NOISES

2004 ◽  
Vol 18 (4) ◽  
pp. 561-571 ◽  
Author(s):  
Naoto Miyoshi
Keyword(s):  
Shot Noise ◽  
Queuing Theory ◽  
Order Relation ◽  
Upper And Lower Bounds ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Doubly Stochastic ◽  
Cox Processes ◽  
Random Intensity ◽  
Monotonicity Result

We consider shot-noise and max-shot-noise processes driven by spatial stationary Cox (doubly stochastic Poisson) processes. We derive their upper and lower bounds in terms of the increasing convex order, which is known as the order relation to compare the variability of random variables. Furthermore, under some regularity assumption of the random intensity fields of Cox processes, we show the monotonicity result which implies that more variable shot patterns lead to more variable shot noises. These are direct applications of the results obtained for so-called Ross-type conjectures in queuing theory.

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