Stochastic Comparison of the Skewness of Parallel Systems in Pareto Model

2018 ◽  
Vol 12 (1) ◽  
pp. 39-55
Author(s):  
Ebrahim Amini-Seresht ◽  
Majid Sadeghifar ◽  
Mona Shiri ◽  
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◽  
...  
Keyword(s):  
Parallel Systems ◽  
Stochastic Comparison ◽  
Pareto Model

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 Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

2018 ◽  
Vol 63 (1) ◽  
pp. 55-77 ◽  
Author(s):  
Lakshmi Kanta Patra ◽  
Suchandan Kayal ◽  
Phalguni Nanda
Keyword(s):  
Parallel Systems ◽  
Stochastic Comparison ◽  
Comparison Results

MONOTONICITY PROPERTIES OF RESIDUAL LIFETIMES OF PARALLEL SYSTEMS AND INACTIVITY TIMES OF SERIES SYSTEMS WITH HETEROGENEOUS COMPONENTS

2011 ◽  
Vol 26 (1) ◽  
pp. 61-75 ◽  
Author(s):  
Weiyong Ding ◽  
Xiaohu Li ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Hazard Rate ◽  
Parallel Systems ◽  
Stochastic Comparison ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Monotonicity Properties ◽  
Series Systems ◽  
Residual Lifetimes

Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16].

LIKELIHOOD RATIO ORDERING OF PARALLEL SYSTEMS WITH HETEROGENEOUS SCALED COMPONENTS

2017 ◽  
Vol 32 (3) ◽  
pp. 460-468 ◽  
Author(s):  
Jiantian Wang
Keyword(s):  
Likelihood Ratio ◽  
Parallel Systems ◽  
New Order ◽  
Stochastic Comparison ◽  
Likelihood Ratio Order ◽  
Generalized Gamma ◽  
Scale Family ◽  
Scale Models ◽  
Likelihood Ratio Ordering

This paper considers stochastic comparison of parallel systems in terms of likelihood ratio order under scale models. We introduce a new order, the so-called q-larger order, and show that under certain conditions, the q-larger order between the scale vectors can imply the likelihood ratio order of parallel systems. Applications are given to the generalized gamma scale family.

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