scholarly journals Joint distribution of new sample rank of bivariate order statistics

2015 ◽  
Vol 42 (10) ◽  
pp. 2280-2289 ◽  
Author(s):  
Gulder Kemalbay ◽  
Ismihan Bayramoglu (Bairamov)
Keyword(s):  
Order Statistics ◽  
Joint Distribution ◽  
Bivariate Order Statistics

Representations and limit theorems for extreme value distributions

1978 ◽  
Vol 15 (03) ◽  
pp. 639-644 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Stochastic Process ◽  
Order Statistics ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Random Variables ◽  
Canonical Representation ◽  
Extreme Value ◽  
Limiting Distribution ◽  
Extreme Value Distributions ◽  
Independent Identically Distributed

LetXn1≦Xn2≦ ··· ≦Xnndenote the order statistics from a sample ofnindependent, identically distributed random variables, and suppose that the variablesXnn, Xn,n–1, ···, when suitably normalized, have a non-trivial limiting joint distributionξ1,ξ2, ···, asn → ∞. It is well known that the limiting distribution must be one of just three types. We provide a canonical representation of the stochastic process {ξn,n≧ 1} in terms of exponential variables, and use this representation to obtain limit theorems forξnasn →∞.

Joint exceedances of high levels under a local dependence condition

1993 ◽  
Vol 30 (01) ◽  
pp. 112-120
Author(s):  
Helena Ferreira
Keyword(s):  
Order Statistics ◽  
Long Range ◽  
Joint Distribution ◽  
Long Range Dependence ◽  
Local Dependence ◽  
Stationary Sequences ◽  
Compound Poisson ◽  
Dependence Conditions

Under appropriate long-range dependence conditions, it is well known that the joint distribution of the number of exceedances of several high levels is asymptotically compound Poisson. Here we investigate the structure of a cluster of exceedances for stationary sequences satisfying a suitable local dependence condition, under which it is only necessary to get certain limiting probabilities, easy to compute, in order to obtain limiting results for the highest order statistics, exceedance counts and upcrossing counts.

scholarly journals Systems with Failure-Dependent Lifetimes of Components

2009 ◽  
Vol 46 (04) ◽  
pp. 1052-1072 ◽  
Author(s):  
M. Burkschat
Keyword(s):  
Order Statistics ◽  
Joint Distribution ◽  
Coherent System ◽  
Coherent Systems ◽  
Sequential Order ◽  
Failure Times ◽  
Sequential Order Statistics ◽  
Definition Of ◽  
General Component

A model for describing the lifetimes of coherent systems, where the failures of components may have an impact on the lifetimes of the remaining components, is proposed. The model is motivated by the definition of sequential order statistics (cf. Kamps (1995)). Sequential order statistics describe the successive failure times in a sequentialk-out-of-nsystem, where the distribution of the remaining components' lifetimes is allowed to change after every failure of a component. In the present paper, general component lifetimes which can be influenced by failures are considered. The ordered failure times of these components can be used to extend the concept of sequential order statistics. In particular, a definition of sequential order statistics based on exchangeable components is proposed. By utilizing the system signature (cf. Samaniego (2007)), the distribution of the lifetime of a coherent system with failure-dependent exchangeable component lifetimes is shown to be given by a mixture of the distributions of sequential order statistics. Furthermore, some results on the joint distribution of sequential order statistics based on exchangeable components are given.

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