LIKELIHOOD RATIO ORDERING OF THE INSPECTION PARADOX

2004 ◽  
Vol 18 (4) ◽  
pp. 503-510 ◽  
Author(s):  
Taizhong Hu ◽  
Weiwei Zhuang
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Likelihood Ratio Ordering

In this article, some results on stochastic comparisons of the inspection paradox introduced by Ross [Probability in the Engineering and Informational Sciences 17: 47–51 (2003)] are established in the sense of the likelihood ratio order.

LIKELIHOOD RATIO AND HAZARD RATE ORDERINGS OF THE MAXIMA IN TWO MULTIPLE-OUTLIER GEOMETRIC SAMPLES

2012 ◽  
Vol 26 (3) ◽  
pp. 375-391 ◽  
Author(s):  
Baojun Du ◽  
Peng Zhao ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Usual Stochastic Order ◽  
Likelihood Ratio Ordering ◽  
Special Case ◽  
Two Parameter

In this paper, we study some stochastic comparisons of the maxima in two multiple-outlier geometric samples based on the likelihood ratio order, hazard rate order, and usual stochastic order. We establish a sufficient condition on parameter vectors for the likelihood ratio ordering to hold. For the special case whenn= 2, it is proved that thep-larger order between the two parameter vectors is equivalent to the hazard rate order as well as usual stochastic order between the two maxima. Some numerical examples are presented for illustrating the established results.

Likelihood ratio comparisons and logconvexity properties of p-spacings from generalized order statistics

2021 ◽  
pp. 1-20
Author(s):  
Mahdi Alimohammadi ◽  
Maryam Esna-Ashari ◽  
Jorge Navarro
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Record Values ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Stochastic Comparisons ◽  
Sequential Order Statistics ◽  
Progressive Type ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$ -spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$ -record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

STOCHASTIC COMPARISONS OF LARGEST ORDER STATISTICS FROM MULTIPLE-OUTLIER EXPONENTIAL MODELS

2012 ◽  
Vol 26 (2) ◽  
pp. 159-182 ◽  
Author(s):  
Peng Zhao ◽  
N. Balakrishnan
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Exponential Models ◽  
Usual Stochastic Order

In this paper, we carry out stochastic comparisons of largest order statistics from multiple-outlier exponential models according to the likelihood ratio order (reversed hazard rate order) and the hazard rate order (usual stochastic order). It is proved, among others, that the weak majorization order between the two hazard rate vectors is equivalent to the likelihood ratio order (reversed hazard rate order) between largest order statistics, and that the p-larger order between the two hazard rate vectors is equivalent to the hazard rate order (usual stochastic order) between largest order statistics. We also extend these results to the proportional hazard rate models. The results established here strengthen and generalize some of the results known in the literature.

scholarly journals Stochastic Comparisons of Residual Lifetimes and Inactivity Times of Coherent Systems

2013 ◽  
Vol 50 (3) ◽  
pp. 848-860 ◽  
Author(s):  
Nitin Gupta
Keyword(s):  
Likelihood Ratio ◽  
Sufficient Conditions ◽  
Structure Functions ◽  
Coherent System ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Likelihood Ratio Ordering ◽  
Necessary And Sufficient ◽  
Residual Lifetimes

Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, for r-out-of-n systems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

COMPARISONS OF SERIES AND PARALLEL SYSTEMS WITH HETEROGENEOUS COMPONENTS

2013 ◽  
Vol 28 (1) ◽  
pp. 39-53 ◽  
Author(s):  
Weiyong Ding ◽  
Gaofeng Da ◽  
Xiaohu Li
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Parallel Systems ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Series Systems

This paper carries out stochastic comparisons of series and parallel systems with independent and heterogeneous components in the sense of the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. The main results extend and strengthen the corresponding ones by Misra and Misra [18] and by Ding, Zhang, and Zhao [8]. Meanwhile, the results on the hazard rate order of parallel systems and the reversed hazard order of series systems serve as nice supplements to Theorem 16.B.1 of Boland and Proschan [4] and Theorem 3.2 of Nanda and Shaked [20], respectively.

Stochastic Comparisons of Residual Lifetimes and Inactivity Times of Coherent Systems

2013 ◽  
Vol 50 (03) ◽  
pp. 848-860 ◽  
Author(s):  
Nitin Gupta
Keyword(s):  
Likelihood Ratio ◽  
Sufficient Conditions ◽  
Structure Functions ◽  
Coherent System ◽  
Stochastic Comparison ◽  
Coherent Systems ◽  
Stochastic Comparisons ◽  
Likelihood Ratio Ordering ◽  
Necessary And Sufficient ◽  
Residual Lifetimes

Under the assumption of independent and identically distributed (i.i.d.) components, the problem of the stochastic comparison of a coherent system having used components and a used coherent system has been considered. Necessary and sufficient conditions on structure functions have been provided for the stochastic comparison of a coherent system having used/inactive i.i.d. components and a used/inactive coherent system. As a consequence, forr-out-of-nsystems, it has been shown that systems having used i.i.d. components stochastically dominate used systems in the likelihood ratio ordering.

SOME NEW RESULTS ON THE LARGEST ORDER STATISTICS FROM MULTIPLE-OUTLIER GAMMA MODELS

2015 ◽  
Vol 29 (4) ◽  
pp. 597-621 ◽  
Author(s):  
Peng Zhao ◽  
Yanni Hu ◽  
Yiying Zhang
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Stochastic Comparisons ◽  
Scale Parameters ◽  
General Sufficient Condition ◽  
Weak Majorization ◽  
Majorization Order ◽  
Star Order ◽  
Theoretical Results

In this paper, we carry out stochastic comparisons of the largest order statistics arising from multiple-outlier gamma models with different both shape and scale parameters in the sense of various stochastic orderings including the likelihood ratio order, star order and dispersive order. It is proved, among others, that the weak majorization order between the scale parameter vectors along with the majorization order between the shape parameter vectors imply the likelihood ratio order between the largest order statistics. A quite general sufficient condition for the star order is presented. The new results established here strengthen and generalize some of the results known in the literature. Numerical examples and applications are also provided to explicate the theoretical results.

UNIVARIATE AND MULTIVARIATE LIKELIHOOD RATIO ORDERING OF GENERALIZED ORDER STATISTICS AND ASSOCIATED CONDITIONAL VARIABLES

2010 ◽  
Vol 24 (3) ◽  
pp. 441-455 ◽  
Author(s):  
Narayanaswamy Balakrishnan ◽  
Félix Belzunce ◽  
Nasrin Hami ◽  
Baha-Eldin Khaledi
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Generalized Order Statistics ◽  
Likelihood Ratio Order ◽  
Likelihood Ratio Ordering ◽  
Multivariate Likelihood ◽  
Special Case ◽  
Generalized Order

In this article, we establish some results concerning the univariate and multivariate likelihood ratio order of generalized order statistics and the special case of m-generalized order statistics and their associated conditional variables. These results, in addition to being new, also generalizes some of the known results in the literature. Finally, some applications of all these results are indicated.

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.

REVISITING MULTIVARIATE LIKELIHOOD RATIO ORDERING RESULTS FOR ORDER STATISTICS

2011 ◽  
Vol 25 (3) ◽  
pp. 355-368 ◽  
Author(s):  
Félix Belzunce ◽  
Selma Gurler ◽  
José M. Ruiz
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Random Vectors ◽  
Dependent Observations ◽  
Likelihood Ratio Ordering ◽  
Multivariate Likelihood

In this article, we establish some results concerning the likelihood ratio order of random vectors of order statistics in the case of independent but not necessarily identically distributed observations and for the case of possible dependent observations. Applications of these results to provide comparisons of conditional order statistics are also given.

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