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 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.

CONDITIONAL ORDERING OF GENERALIZED ORDER STATISTICS REVISITED

2008 ◽  
Vol 22 (3) ◽  
pp. 333-346 ◽  
Author(s):  
Hongmei Xie ◽  
Taizhong Hu
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Order Statistic ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Likelihood Ratio Ordering ◽  
The Right ◽  
Generalized Order

In this article we investigate less restrictive conditions on the model parameters that enable one to establish the likelihood ratio ordering of one generalized order statistic by conditioning on the right tail of another lower-indexed generalized order statistic. One application of the main results is also presented.

STOCHASTIC ORDERINGS BETWEEN p-SPACINGS OF GENERALIZED ORDER STATISTICS FROM TWO SAMPLES

2006 ◽  
Vol 20 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Taizhong Hu ◽  
Weiwei Zhuang
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Unified Approach ◽  
Stochastic Orderings ◽  
Two Samples ◽  
Likelihood Ratio Ordering ◽  
Generalized Order

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to investigate conditions on the distributions and the parameters on which the generalized order statistics are based to establish the likelihood ratio ordering of general p-spacings and the hazard rate and the dispersive orderings of (normalizing) simple spacings from two samples. We thus strengthen and complement some results in Franco, Ruiz, and Ruiz [7] and Belzunce, Mercader, and Ruiz [5]. This article is a continuation of Hu and Zhuang [10].

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.

ORDERING CONDITIONAL DISTRIBUTIONS OF GENERALIZED ORDER STATISTICS

2007 ◽  
Vol 21 (3) ◽  
pp. 401-417 ◽  
Author(s):  
Taizhong Hu ◽  
Wei Jin ◽  
Baha-Eldin Khaledi
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Conditional Distributions ◽  
Unified Approach ◽  
Two Samples ◽  
Generalized Order

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to establish the usual stochastic and the likelihood ratio orderings of conditional distributions of generalized order statistics from one sample or two samples, strengthening and generalizing the main results in Khaledi and Shaked [15], and Li and Zhao [17]. Some applications of the main results are also given.

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.

ORDERING p-SPACINGS OF GENERALIZED ORDER STATISTICS REVISITED

2008 ◽  
Vol 23 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Hongmei Xie ◽  
Taizhong Hu
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Likelihood Ratio ◽  
Order Statistic ◽  
Hazard Ratio ◽  
Generalized Order Statistics ◽  
Model Parameters ◽  
Underlying Distribution ◽  
Generalized Order

In this article we investigate less restrictive conditions on the model parameters and the underlying distribution function upon which the generalized order statistics are based, which enable one to establish the likelihood ratio and the hazard ratio orderings for p-spacings of generalized order statistic. Some previous works in the literature are extended.

STOCHASTIC PROPERTIES OF p-SPACINGS OF GENERALIZED ORDER STATISTICS

2005 ◽  
Vol 19 (2) ◽  
pp. 257-276 ◽  
Author(s):  
Taizhong Hu ◽  
Weiwei Zhuang
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Generalized Order Statistics ◽  
Unified Approach ◽  
Stochastic Comparisons ◽  
Stochastic Properties ◽  
Generalized Order

The concept of generalized order statistics was introduced as a unified approach to a variety of models of ordered random variables. The purpose of this article is to investigate the conditions on the parameters that enable one to establish several stochastic comparisons of general p-spacings for a subclass of generalized order statistics in the likelihood ratio and the hazard rate orders. Preservation properties of the logconvexity and logconcavity of p-spacings are also given.

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