scholarly journals Dispersive order comparisons on extreme order statistics from homogeneous dependent random vectors

2021 ◽  
Vol 9 (1) ◽  
pp. 385-393
Author(s):  
Mhamed Mesfioui ◽  
Julien Trufin
Keyword(s):  
Order Statistics ◽  
Sufficient Conditions ◽  
Random Vectors ◽  
Dispersive Order ◽  
Extreme Order Statistics ◽  
Preservation Property

Abstract In this paper, we investigate sufficient conditions for preservation property of the dispersive order for the smallest and largest order statistics of homogeneous dependent random vectors. Moreover, we establish sufficient conditions for ordering with the dispersive order the largest order statistics from dependent homogeneous samples of different sizes.

On stochastic comparison of random vectors

1987 ◽  
Vol 24 (1) ◽  
pp. 123-136 ◽  
Author(s):  
J. George Shanthikumar
Keyword(s):  
Partial Order ◽  
Order Statistics ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Comparison ◽  
Stochastic Monotonicity ◽  
Random Vectors ◽  
Standard Construction ◽  
Frequency Functions ◽  
Independent And Identically Distributed

We provide sufficient conditions under which two random vectors could be stochastically compared using the standard construction. These conditions are weaker than those discussed by Arjas and Lehtonen (1978) and Veinott (1965). Using these conditions we present extensions of (i) a result of Block et al. (1984) concerning the stochastic monotonicity of independent and identically distributed random variables conditioned on their partial order statistics, and (ii) a theorem of Efron (1965) regarding an increasing property of Pólya frequency functions. Applications of these extensions are also pointed out.

On stochastic comparison of random vectors

1987 ◽  
Vol 24 (01) ◽  
pp. 123-136 ◽  
Author(s):  
J. George Shanthikumar
Keyword(s):  
Partial Order ◽  
Order Statistics ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Comparison ◽  
Stochastic Monotonicity ◽  
Random Vectors ◽  
Standard Construction ◽  
Frequency Functions ◽  
Independent And Identically Distributed

We provide sufficient conditions under which two random vectors could be stochastically compared using the standard construction. These conditions are weaker than those discussed by Arjas and Lehtonen (1978) and Veinott (1965). Using these conditions we present extensions of (i) a result of Block et al. (1984) concerning the stochastic monotonicity of independent and identically distributed random variables conditioned on their partial order statistics, and (ii) a theorem of Efron (1965) regarding an increasing property of Pólya frequency functions. Applications of these extensions are also pointed out.

On sufficient conditions for the comparison in the excess wealth order and spacings

2016 ◽  
Vol 53 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Félix Belzunce ◽  
Carolina Martínez-Riquelme ◽  
José M. Ruiz ◽  
Miguel A. Sordo
Keyword(s):  
Order Statistics ◽  
Sufficient Conditions ◽  
The Other ◽  
Generalized Order Statistics ◽  
Convex Order ◽  
Increasing Convex Order ◽  
Dispersive Order ◽  
Excess Wealth Order ◽  
The One ◽  
Quantities Of Interest

Abstract The purpose of this paper is twofold. On the one hand, we provide sufficient conditions for the excess wealth order. These conditions are based on properties of the quantile functions which are useful when the dispersive order does not hold. On the other hand, we study sufficient conditions for the comparison in the increasing convex order of spacings of generalized order statistics. These results will be combined to show how we can provide comparisons of quantities of interest in reliability and insurance.

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-𝑟+ 1)-out-of-𝑛 systems

2018 ◽  
Vol 55 (3) ◽  
pp. 834-844
Author(s):  
Ghobad Barmalzan ◽  
Abedin Haidari ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Order Statistics ◽  
Exponential Distribution ◽  
Sufficient Conditions ◽  
Sequential Order ◽  
Stochastic Orderings ◽  
Sequential Order Statistics ◽  
Residual Lifetimes

Abstract Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.

Order statistics, Poisson processes and repairable systems

1976 ◽  
Vol 13 (03) ◽  
pp. 519-529 ◽  
Author(s):  
Douglas R. Miller
Keyword(s):  
Order Statistics ◽  
Point Processes ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Renewal Processes ◽  
Repairable Systems ◽  
Homogeneous Poisson Process ◽  
Necessary And Sufficient ◽  
Non Homogeneous Poisson Process ◽  
Weibull Process

Necessary and sufficient conditions are presented under which the point processes equivalent to order statistics of n i.i.d. random variables or superpositions of n i.i.d. renewal processes converge to a non-degenerate limiting process as n approaches infinity. The limiting process must be one of three types of non-homogeneous Poisson process, one of which is the Weibull process. These point processes occur as failure-time models in the reliability theory of repairable systems.

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