Dispersive ordering—Some applications and examples

2006 ◽  
Vol 47 (2) ◽  
pp. 227-247 ◽  
Author(s):  
Jongwoo Jeon ◽  
Subhash Kochar ◽  
Chul Gyu Park
Keyword(s):  
Dispersive Ordering

Dispersive Ordering Results.

1983 ◽  
Author(s):  
James Lynch ◽  
Frank Proschan
Keyword(s):  
Dispersive Ordering

Stochastic comparison of parallel systems with Pareto components

2021 ◽  
pp. 1-13
Author(s):  
Sameen Naqvi ◽  
Weiyong Ding ◽  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Extreme Value Theory ◽  
Pareto Distribution ◽  
Parallel Systems ◽  
Value Theory ◽  
Extreme Value ◽  
Stochastic Comparison ◽  
Shape Parameters ◽  
Scale Parameters ◽  
Dispersive Ordering

Abstract Pareto distribution is an important distribution in extreme value theory. In this paper, we consider parallel systems with Pareto components and study the effect of heterogeneity on skewness of such systems. It is shown that, when the lifetimes of components have different shape parameters, the parallel system with heterogeneous Pareto component lifetimes is more skewed than the system with independent and identically distributed Pareto components. However, for the case when the lifetimes of components have different scale parameters, the result gets reversed in the sense of star ordering. We also establish the relation between star ordering and dispersive ordering by extending the result of Deshpande and Kochar [(1983). Dispersive ordering is the same as tail ordering. Advances in Applied Probability 15(3): 686–687] from support $(0, \infty )$ to general supports $(a, \infty )$ , $a > 0$ . As a consequence, we obtain some new results on dispersion of order statistics from heterogeneous Pareto samples with respect to dispersive ordering.

scholarly journals Dispersive ordering results

1983 ◽  
Vol 15 (04) ◽  
pp. 889-891 ◽  
Author(s):  
James Lynch ◽  
Gillian Mimmack ◽  
Frank Proschan
Keyword(s):  
Simple Proof ◽  
Total Positivity ◽  
Sign Changes ◽  
Dispersive Ordering

A distribution F is less dispersed than a distribution G if for all . We generalize a characterization of dispersive ordering of Shaked (1982) concerning sign changes of Fc – G, where Fc is a translate of F. We then use this generalization plus total positivity to develop a simple proof of a characterization of dispersive distributions due to Lewis and Thompson (1981); a distribution H is dispersive if

scholarly journals Dispersive ordering is the same as tail-ordering

1983 ◽  
Vol 15 (03) ◽  
pp. 686-687 ◽  
Author(s):  
J. V. Deshpande ◽  
S. C. Kochar
Keyword(s):  
Dispersive Ordering

Partial Orderings of Distributions Based on Right-Spread Functions

1998 ◽  
Vol 35 (1) ◽  
pp. 221-228 ◽  
Author(s):  
J. M. Fernandez-Ponce ◽  
S. C. Kochar ◽  
J. Muñoz-Perez
Keyword(s):  
Probability Distributions ◽  
Partial Ordering ◽  
Dispersion Measure ◽  
Dispersive Ordering ◽  
Partial Orderings

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.

scholarly journals Dispersive and superadditive ordering

1986 ◽  
Vol 18 (4) ◽  
pp. 1019-1022 ◽  
Author(s):  
A. N. Ahmed ◽  
A. Alzaid ◽  
J. Bartoszewicz ◽  
S. C. Kochar
Keyword(s):  
Dispersive Ordering ◽  
Partial Orderings

Recently many authors have established connections between dispersive ordering and some other partial orderings of distributions. This paper presents the connection which superadditive ordering has with dispersive ordering.

scholarly journals Dispersive ordering of fail-safe systems with heterogeneous exponential components

Metrika ◽  
2010 ◽  
Vol 74 (2) ◽  
pp. 203-210 ◽  
Author(s):  
Peng Zhao ◽  
N. Balakrishnan
Keyword(s):  
Dispersive Ordering ◽  
Fail Safe

scholarly journals Dispersive ordering results

1983 ◽  
Vol 15 (4) ◽  
pp. 889-891 ◽  
Author(s):  
James Lynch ◽  
Gillian Mimmack ◽  
Frank Proschan
Keyword(s):  
Simple Proof ◽  
Total Positivity ◽  
Sign Changes ◽  
Dispersive Ordering

A distribution F is less dispersed than a distribution G if for all .We generalize a characterization of dispersive ordering of Shaked (1982) concerning sign changes of Fc – G, where Fc is a translate of F. We then use this generalization plus total positivity to develop a simple proof of a characterization of dispersive distributions due to Lewis and Thompson (1981); a distribution H is dispersive if

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