Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables

2009 ◽  
Vol 79 (15) ◽  
pp. 1717-1723 ◽  
Author(s):  
Peng Zhao ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Random Variables ◽  
Likelihood Ratio Ordering

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].

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.

scholarly journals Stochastic Order Relations Among Parallel Systems from Weibull Distributions

2015 ◽  
Vol 52 (01) ◽  
pp. 102-116 ◽  
Author(s):  
Nuria Torrado ◽  
Subhash C. Kochar
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Variables ◽  
Parallel Systems ◽  
Parallel System ◽  
Weibull Distributions ◽  
Scale Parameters ◽  
Order Relations ◽  
Stochastic Order Relations

Let X λ1 , X λ2 , …, X λ n be independent Weibull random variables with X λ i ∼ W(α, λ i ), where λ i > 0 for i = 1, …, n. Let X n:n λ denote the lifetime of the parallel system formed from X λ1 , X λ2 , …, X λ n . We investigate the effect of the changes in the scale parameters (λ1, …, λ n ) on the magnitude of X n:n λ according to reverse hazard rate and likelihood ratio orderings.

scholarly journals A star-like circuit-switching network with multistage service

1990 ◽  
Vol 22 (04) ◽  
pp. 965-967
Author(s):  
Z. Khalil ◽  
G. Falin
Keyword(s):  
Likelihood Ratio ◽  
Optimal Threshold ◽  
Switching Network ◽  
Circuit Switching ◽  
Traffic Intensity ◽  
Likelihood Ratio Ordering ◽  
The Mean

A star-like circuit-switching network with multistage service is considered. Likelihood ratio ordering is used to show that there exists an optimal threshold for the mean number of messages processed through the network as a function of the input traffic intensity.

scholarly journals On the Convolution of Heterogeneous Bernoulli Random Variables

2011 ◽  
Vol 48 (3) ◽  
pp. 877-884 ◽  
Author(s):  
Maochao Xu ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Random Variables ◽  
Likelihood Ratio Order ◽  
Hazard Rate Order ◽  
Reversed Hazard Rate ◽  
Bernoulli Random Variables

In this paper, some ordering properties of convolutions of heterogeneous Bernoulli random variables are discussed. It is shown that, under some suitable conditions, the likelihood ratio order and the reversed hazard rate order hold between convolutions of two heterogeneous Bernoulli sequences. The results established here extend and strengthen the previous results of Pledger and Proschan (1971) and Boland, Singh and Cukic (2002).

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.

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