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

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.

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 ◽  
◽  
◽  
...  
Keyword(s):  
Parallel Systems ◽  
Stochastic Comparison ◽  
Pareto Model

scholarly journals Comparison Results for GARCH Processes

2014 ◽  
Vol 51 (3) ◽  
pp. 685-698
Author(s):  
Fabio Bellini ◽  
Franco Pellerey ◽  
Carlo Sgarra ◽  
Salimeh Yasaei Sekeh
Keyword(s):  
Stochastic Orders ◽  
Stochastic Comparison ◽  
Convex Order ◽  
Comparison Results ◽  
Garch Processes ◽  
Garch Process

We consider the problem of stochastic comparison of general GARCH-like processes for different parameters and different distributions of the innovations. We identify several stochastic orders that are propagated from the innovations to the GARCH process itself, and we discuss their interpretations. We focus on the convex order and show that in the case of symmetric innovations it is also propagated to the cumulated sums of the GARCH process. More generally, we discuss multivariate comparison results related to the multivariate convex and supermodular orders. Finally, we discuss ordering with respect to the parameters in the GARCH(1, 1) case.

Stochastic comparison of repairable systems by coupling

1998 ◽  
Vol 35 (2) ◽  
pp. 348-370 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Point Processes ◽  
Stochastic Comparison ◽  
Repairable Systems ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Comparison Results ◽  
Special Cases ◽  
Repair Models

Stochastic comparison results for replacement policies are shown in this paper using the formalism of point processes theory. At each failure moment a repair is allowed. It is performed with a random degree of repair including (as special cases) perfect, minimal and imperfect repair models. Results for such repairable systems with schemes of planned replacements are also shown. The results are obtained by coupling methods for point processes.

scholarly journals Stochastic Epidemic Models in Structured Populations Featuring Dynamic Vaccination and Isolation

2007 ◽  
Vol 44 (03) ◽  
pp. 571-585 ◽  
Author(s):  
Frank Ball ◽  
Philip D. O'Neill ◽  
James Pike
Keyword(s):  
Exposure Period ◽  
Structured Populations ◽  
Infectious Period ◽  
Stochastic Comparison ◽  
Threshold Parameter ◽  
Final Size ◽  
Period Distribution ◽  
Comparison Results ◽  
Stochastic Epidemic ◽  
Large Populations

We consider a stochastic model for the spread of an SEIR (susceptible → exposed → infective → removed) epidemic among a population of individuals partitioned into households. The model incorporates both vaccination and isolation in response to the detection of cases. When the infectious period is exponential, we derive an explicit formula for a threshold parameter, and analytic results that enable computation of the probability of the epidemic taking off. These quantities are found to be independent of the exposure period distribution. An approximation for the expected final size of an epidemic that takes off is obtained, evaluated numerically, and found to be reasonably accurate in large populations. When the infectious period is not exponential, but has an increasing hazard rate, we obtain stochastic comparison results in the case where the exposure period is fixed. Our main result shows that as the exposure period increases, both the severity of the epidemic in a single household and the threshold parameter decrease, under certain assumptions concerning isolation. Corresponding results for infectious periods with decreasing hazard rates are also derived.

scholarly journals Stochastic Epidemic Models in Structured Populations Featuring Dynamic Vaccination and Isolation

2007 ◽  
Vol 44 (3) ◽  
pp. 571-585 ◽  
Author(s):  
Frank Ball ◽  
Philip D. O'Neill ◽  
James Pike
Keyword(s):  
Exposure Period ◽  
Structured Populations ◽  
Infectious Period ◽  
Stochastic Comparison ◽  
Threshold Parameter ◽  
Final Size ◽  
Period Distribution ◽  
Comparison Results ◽  
Stochastic Epidemic ◽  
Large Populations

We consider a stochastic model for the spread of an SEIR (susceptible → exposed → infective → removed) epidemic among a population of individuals partitioned into households. The model incorporates both vaccination and isolation in response to the detection of cases. When the infectious period is exponential, we derive an explicit formula for a threshold parameter, and analytic results that enable computation of the probability of the epidemic taking off. These quantities are found to be independent of the exposure period distribution. An approximation for the expected final size of an epidemic that takes off is obtained, evaluated numerically, and found to be reasonably accurate in large populations. When the infectious period is not exponential, but has an increasing hazard rate, we obtain stochastic comparison results in the case where the exposure period is fixed. Our main result shows that as the exposure period increases, both the severity of the epidemic in a single household and the threshold parameter decrease, under certain assumptions concerning isolation. Corresponding results for infectious periods with decreasing hazard rates are also derived.

scholarly journals Trend-transformed independent vectors: construction and stochastic comparison results

Statistics ◽  
2020 ◽  
Vol 54 (4) ◽  
pp. 778-804
Author(s):  
F. G. Badía ◽  
Sophie Mercier ◽  
C. Sangüesa
Keyword(s):  
Stochastic Comparison ◽  
Comparison Results

Stochastic comparisons of random minima and maxima

1997 ◽  
Vol 34 (02) ◽  
pp. 420-425 ◽  
Author(s):  
Moshe Shaked ◽  
Tityik Wong
Keyword(s):  
Positive Integer ◽  
Random Variables ◽  
Random Variable ◽  
Independent Random Variables ◽  
Stochastic Comparison ◽  
Stochastic Comparisons ◽  
Comparison Results

Let X 1, X 2,… be a sequence of independent random variables and let N be a positive integer-valued random variable which is independent of the Xi. In this paper we obtain some stochastic comparison results involving min {X 1, X 2,…, XN ) and max{X 1, X 2,…, XN }.

Orderings of component level versus system level at active redundancies for coherent systems with dependent components

2021 ◽  
pp. 1-23
Author(s):  
Rongfang Yan ◽  
Junrui Wang ◽  
Bin Lu
Keyword(s):  
Hazard Rate ◽  
System Level ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Component Level ◽  
Comparison Results ◽  
Versus System ◽  
Level Versus ◽  
Theoretical Results ◽  
Complete Matching

This paper investigates the issue of stochastic comparison of multi-active redundancies at the component level versus the system level. Based on the assumption that all components are statistically dependent, in the case of complete matching and nonmatching spares, we present some interesting comparison results in the sense of the hazard rate, reversed hazard rate and likelihood ratio orders, respectively. And we also obtain two comparison results between relative agings of resulting systems at the component level and the system level. Several numerical examples are provided to illustrate the theoretical results.

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