Limit Theorems for Order Statistics with Variable Rank Under Exponential Normalization

Sankhya A ◽  
2022 ◽  
Author(s):  
H. M. Barakat ◽  
A. R. Omar
Keyword(s):  
Order Statistics ◽  
Limit Theorems

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 →∞.

Limit theorems for order statistics from exponentials

2016 ◽  
Vol 110 ◽  
pp. 51-57 ◽  
Author(s):  
Yu Miao ◽  
Rujun Wang ◽  
Andre Adler
Keyword(s):  
Order Statistics ◽  
Limit Theorems

scholarly journals Various limit theorems for ratios from the uniform distribution

2016 ◽  
Vol 14 (1) ◽  
pp. 393-403 ◽  
Author(s):  
Yu Miao ◽  
Yan Sun ◽  
Rujun Wang ◽  
Manru Dong
Keyword(s):  
Order Statistics ◽  
Uniform Distribution ◽  
Limit Theorems ◽  
Weak Laws

AbstractIn this paper, we consider the ratios of order statistics in samples from uniform distribution and establish strong and weak laws for these ratios.

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