On a new positive dependence concept based on the conditional mean inactivity time order

2016 ◽  
Vol 46 (4) ◽  
pp. 1779-1787
Author(s):  
Z. Zamani ◽  
G. R. Mohtashami Borzadaran ◽  
M. Amini
Keyword(s):  
Positive Dependence ◽  
Conditional Mean ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time

CHARACTERIZATIONS OF THE RHR AND MIT ORDERINGS AND THE DRHR AND IMIT CLASSES OF LIFE DISTRIBUTIONS

2005 ◽  
Vol 19 (4) ◽  
pp. 447-461 ◽  
Author(s):  
I. A. Ahmad ◽  
M. Kayid
Keyword(s):  
Hazard Rate ◽  
Stochastic Comparison ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
The Mean ◽  
Decreasing Reversed Hazard Rate

Two well-known orders that have been introduced and studied in reliability theory are defined via stochastic comparison of inactivity time: the reversed hazard rate order and the mean inactivity time order. In this article, some characterization results of those orders are given. We prove that, under suitable conditions, the reversed hazard rate order is equivalent to the mean inactivity time order. We also provide new characterizations of the decreasing reversed hazard rate (increasing mean inactivity time) classes based on variability orderings of the inactivity time of k-out-of-n system given that the time of the (n − k + 1)st failure occurs at or sometimes before time t ≥ 0. Similar conclusions based on the inactivity time of the component that fails first are presented as well. Finally, some useful inequalities and relations for weighted distributions related to reversed hazard rate (mean inactivity time) functions are obtained.

scholarly journals Increasing Mean Inactivity Time Ordering: A Quantile Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
M. Kayid ◽  
S. Izadkhah ◽  
A. Alfifi
Keyword(s):  
Stochastic Order ◽  
Sufficient Conditions ◽  
Parallel Systems ◽  
The Other ◽  
Stochastic Orders ◽  
General Family ◽  
Order Relations ◽  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time

We study further the quantile mean inactivity time order. Relations between the proposed stochastic order and the other transform stochastic orders are obtained. Besides, sufficient conditions for the stochastic order are provided. Then, preservation of the order under monotone transformations, series, and parallel systems and mixtures of a general family of semiparametric distributions is studied. Examples are also given to illustrate the results.

Development on the mean inactivity time order with applications

2017 ◽  
Vol 45 (5) ◽  
pp. 525-529 ◽  
Author(s):  
M. Kayid ◽  
S. Izadkhah ◽  
S. Alshami
Keyword(s):  
Inactivity Time ◽  
Time Order ◽  
Mean Inactivity Time ◽  
The Mean

SOME RESULTS ABOUT MIT ORDER AND IMIT CLASS OF LIFE DISTRIBUTIONS

2006 ◽  
Vol 20 (3) ◽  
pp. 481-496 ◽  
Author(s):  
Xiaohu Li ◽  
Maochao Xu
Keyword(s):  
Renewal Process ◽  
Residual Life ◽  
Random Time ◽  
Mean Residual Life ◽  
Stochastic Comparisons ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Life Distributions ◽  
Preservation Property

We investigate some new properties of mean inactivity time (MIT) order and increasing MIT (IMIT) class of life distributions. The preservation property of MIT order under increasing and concave transformations, reversed preservation properties of MIT order, and IMIT class of life distributions under the taking of maximum are developed. Based on the residual life at a random time and the excess lifetime in a renewal process, stochastic comparisons of both IMIT and decreasing mean residual life distributions are conducted as well.

scholarly journals Weighted proportional mean inactivity time model

2021 ◽  
Vol 7 (3) ◽  
pp. 4038-4060
Author(s):  
Mohamed Kayid ◽  
◽  
Adel Alrasheedi
Keyword(s):  
Frailty Model ◽  
Real Data ◽  
Survival Models ◽  
Dependence Structure ◽  
Time Model ◽  
Data Set ◽  
Population Variable ◽  
Inactivity Time ◽  
Mean Inactivity Time ◽  
Special Case

<abstract><p>In this paper, a mean inactivity time frailty model is considered. Examples are given to calculate the mean inactivity time for several reputable survival models. The dependence structure between the population variable and the frailty variable is characterized. The classical weighted proportional mean inactivity time model is considered as a special case. We prove that several well-known stochastic orderings between two frailties are preserved for the response variables under the weighted proportional mean inactivity time model. We apply this model on a real data set and also perform a simulation study to examine the accuracy of the model.</p></abstract>

Testing Behavior of the Mean Inactivity Time

2018 ◽  
Vol 46 (6) ◽  
pp. 20160611
Author(s):  
M. Kayid ◽  
S. Izadkhah
Keyword(s):  
Inactivity Time ◽  
Mean Inactivity Time ◽  
The Mean
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