scholarly journals Two-Sided Estimates for Order Statistics of Log-Concave Random Vectors

2020 ◽  
pp. 65-94
Author(s):  
Rafał Latała ◽  
Marta Strzelecka
Keyword(s):  
Order Statistics ◽  
Random Vectors

scholarly journals Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
K. Müller ◽  
W.-D. Richter
Keyword(s):  
Computer Program ◽  
Order Statistics ◽  
Stock Exchange ◽  
Random Variables ◽  
Integral Representations ◽  
Symmetric Distribution ◽  
Random Vectors ◽  
Dependent Random Variables ◽  
Exact Distributions

AbstractIntegral representations of the exact distributions of order statistics are derived in a geometric way when three or four random variables depend on each other as the components of continuous ln,psymmetrically distributed random vectors do, n ∈ {3,4}, p > 0. Once the representations are implemented in a computer program, it is easy to change the density generator of the ln,p-symmetric distribution with another one for newly evaluating the distribution of interest. For two groups of stock exchange index residuals, maximum distributions are compared under dependence and independence modeling.

Multivariate properties of random vectors of order statistics

2003 ◽  
Vol 115 (2) ◽  
pp. 413-424 ◽  
Author(s):  
Félix Belzunce ◽  
José-Marı́a Ruiz ◽  
Marı́a-del-Carmen Ruiz
Keyword(s):  
Order Statistics ◽  
Random Vectors

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.

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