scholarly journals Dependence Concepts and Reliability Application of Concomitants of Order Statistics from the Morgenstern Family

2021 ◽  
Author(s):  
Johny Scaria ◽  
Sithara Mohan
Keyword(s):  
Order Statistics ◽  
Concomitants Of Order Statistics ◽  
Dependence Concepts

The asymptotic theory of concomitants of order statistics

1974 ◽  
Vol 11 (04) ◽  
pp. 762-770 ◽  
Author(s):  
H. A. David ◽  
J. Galambos
Keyword(s):  
Order Statistics ◽  
Asymptotic Distribution ◽  
Random Sample ◽  
Order Statistic ◽  
Asymptotic Theory ◽  
Selection Procedures ◽  
Concomitants Of Order Statistics ◽  
Bivariate Normal ◽  
Independent Identically Distributed

In a random sample of n pairs (X r , Y r ), r = 1, 2, …, n, drawn from a bivariate normal distribution, let Xr :n be the rth order statistic among the Xr and let Y [r:n] be the Y-variate paired with Xr :n . The Y[r:n] , which we call concomitants of the order statistics, arise most naturally in selection procedures based on the Xr :n . It is shown that asymptotically the k quantities k fixed, are independent, identically distributed variates. In addition, putting Rt,n for the number of integers j for which , the asymptotic distribution and all moments of n– 1 Rt, n are determined for t such that t/n → λ with 0 < λ < 1.

Asymptotic Normality of a Class of Nonparametric Statistics

1987 ◽  
Vol 3 (3) ◽  
pp. 313-347 ◽  
Author(s):  
Munsup Seoh ◽  
Madan L. Puri
Keyword(s):  
Asymptotic Normality ◽  
Order Statistics ◽  
Linear Combination ◽  
Linear Function ◽  
Random Variables ◽  
Weighted Sum ◽  
Rank Statistics ◽  
Concomitants Of Order Statistics ◽  
Signed Rank ◽  
Special Cases

Asymptotic normality is established for a class of statistics which includes as special cases weighted sum of independent and identically distributed (i.i.d.) random variables, unsigned linear rank statistics, signed rank statistics, linear combination of functions of order statistics, and linear function of concomitants of order statistics. The results obtained unify as well as extend a number of known results.

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