scholarly journals Stochastic Comparisons of Order Statistics and Spacings: A Review

2012 ◽  
Vol 2012 ◽  
pp. 1-47 ◽  
Author(s):  
Subhash Kochar
Keyword(s):  
Order Statistics ◽  
Hazard Rate ◽  
Proportional Hazard ◽  
Rate Model ◽  
Stochastic Comparisons ◽  
Scale Parameters ◽  
Hazard Rate Model ◽  
Recent Developments ◽  
Parent Observations ◽  
Sample Spacings

We review some of the recent developments in the area of stochastic comparisons of order statistics and sample spacings. We consider the cases when the parent observations are identically as well as nonidentically distributed. But most of the time we will be assuming that the observations are independent. The case of independent exponentials with unequal scale parameters as well as the proportional hazard rate model is discussed in detail.

Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications

2020 ◽  
Vol 57 (3) ◽  
pp. 832-852
Author(s):  
Lu Li ◽  
Qinyu Wu ◽  
Tiantian Mao
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Parallel Systems ◽  
Rate Model ◽  
Stochastic Comparisons ◽  
Reversed Hazard Rate ◽  
Generalized Gamma ◽  
Pareto Distributions ◽  
Hazard Rate Model

AbstractWe investigate stochastic comparisons of parallel systems (corresponding to the largest-order statistics) with respect to the reversed hazard rate and likelihood ratio orders for the proportional reversed hazard rate (PRHR) model. As applications of the main results, we obtain the equivalent characterizations of stochastic comparisons with respect to the reversed hazard rate and likelihood rate orders for the exponentiated generalized gamma and exponentiated Pareto distributions. Our results recover and strengthen some recent results in the literature.

Railway Passengers Travel Time Research Based on Survival Analysis

2014 ◽  
Vol 962-965 ◽  
pp. 2580-2583
Author(s):  
Ya Chen Zhao ◽  
Zhen Yu Zhang ◽  
Qing Jie Zheng
Keyword(s):  
Survival Analysis ◽  
Travel Time ◽  
Significant Influence ◽  
Hazard Rate ◽  
Family Income ◽  
Proportional Hazard ◽  
Rate Model ◽  
Analysis Method ◽  
Cox Proportional Hazard ◽  
Hazard Rate Model

With the development of the economy, people have higher request for the time. Studying the choice of travel about rail passengers becomes more significant. Due to these problem above and using survival analysis method, this paper builds travel time survival model based on questionnaire and have a whole analysis of the travel time of the rail passenger. Then, it concludes that most of the rail passengers’ travel time is below five hours. At last, this paper builds COX proportional hazard rate model of travel time and study the factors about travel time. The result demonstrates that the factor about whether it is students or not, family income, whether it is travelling and the number of packages has a significant influence on the travel time.

scholarly journals Comparisons of Parallel Systems According to the Convex Transform Order

2009 ◽  
Vol 46 (2) ◽  
pp. 342-352 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Hazard Rate ◽  
Parallel Systems ◽  
Sufficient Condition ◽  
Proportional Hazard ◽  
Rate Model ◽  
Hazard Rate Model ◽  
Convex Transform Order ◽  
Right Spread Order ◽  
The Right ◽  
Equivalent Conditions

A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics from heterogeneous and homogeneous exponential samples in the sense of the dispersive order and the right-spread order are established. A sufficient condition is also given for the proportional hazard rate model.

scholarly journals Comparisons of Parallel Systems According to the Convex Transform Order

2009 ◽  
Vol 46 (02) ◽  
pp. 342-352 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Hazard Rate ◽  
Parallel Systems ◽  
Sufficient Condition ◽  
Proportional Hazard ◽  
Rate Model ◽  
Hazard Rate Model ◽  
Convex Transform Order ◽  
Right Spread Order ◽  
The Right ◽  
Equivalent Conditions

A parallel system with heterogeneous exponential component lifetimes is shown to be more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. As a consequence, equivalent conditions for comparing the variabilities of the largest order statistics from heterogeneous and homogeneous exponential samples in the sense of the dispersive order and the right-spread order are established. A sufficient condition is also given for the proportional hazard rate model.

Parametric inference from system lifetime data under a proportional hazard rate model

Metrika ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. 367-388 ◽  
Author(s):  
Hon Keung Tony Ng ◽  
Jorge Navarro ◽  
Narayanaswamy Balakrishnan
Keyword(s):  
Hazard Rate ◽  
Lifetime Data ◽  
Proportional Hazard ◽  
Rate Model ◽  
Parametric Inference ◽  
Hazard Rate Model ◽  
System Lifetime Data
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