Likelihood ratio order of sample minimum from heterogeneous Weibull random variables

2015 ◽  
Vol 97 ◽  
pp. 46-53 ◽  
Author(s):  
Chen Li ◽  
Xiaohu Li
Keyword(s):  
Likelihood Ratio ◽  
Random Variables ◽  
Likelihood Ratio Order ◽  
Sample Minimum

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).

ON PARALLEL SYSTEMS WITH HETEROGENEOUS GAMMA COMPONENTS

2011 ◽  
Vol 25 (3) ◽  
pp. 369-391 ◽  
Author(s):  
Peng Zhao
Keyword(s):  
Order Statistics ◽  
Likelihood Ratio ◽  
Hazard Rate ◽  
Shape Parameter ◽  
Scale Parameter ◽  
Random Variables ◽  
Parallel Systems ◽  
Likelihood Ratio Order ◽  
Maximum Order ◽  
Hazard Rate Order

In this article, we study ordering properties of lifetimes of parallel systems with two independent heterogeneous gamma components in terms of the likelihood ratio order and the hazard rate order. LetX1andX2be two independent gamma random variables withXihaving shape parameterr>0 and scale parameter λi,i=1, 2, and letX*1andX*2be another set of independent gamma random variables withX*ihaving shape parameterrand scale parameter λ*i,i=1, 2. Denote byX2:2andX*2:2the corresponding maximum order statistics, respectively. It is proved that, among others, if (λ1, λ2) weakly majorize (λ*1, λ*2), thenX2:2is stochastically greater thanX*2:2in the sense of likelihood ratio order. We also establish, among others, that if 0<r≤1 and (λ1, λ2) isp-larger than (λ*1, λ*2), thenX2:2is stochastically greater thanX*2:2in the sense of hazard rate order. The results derived here strengthen and generalize some of the results known in the literature.

scholarly journals On the Convolution of Heterogeneous Bernoulli Random Variables

2011 ◽  
Vol 48 (03) ◽  
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).

scholarly journals Stochastic monotonicity of dependent variables given their sum

Test ◽  
2021 ◽  
Author(s):  
Franco Pellerey ◽  
Jorge Navarro
Keyword(s):  
Likelihood Ratio ◽  
Random Variables ◽  
Monotonicity Property ◽  
Expected Value ◽  
Independent Random Variables ◽  
Likelihood Ratio Order ◽  
Stochastic Monotonicity ◽  
Dependent Variables ◽  
Finite Set

AbstractGiven a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.

New Stochastic Orders Based on Double Truncation

1997 ◽  
Vol 11 (3) ◽  
pp. 395-402 ◽  
Author(s):  
Jorge Navarro ◽  
Felix Belzunce ◽  
Jose M. Ruiz
Keyword(s):  
Likelihood Ratio ◽  
Random Variable ◽  
Stochastic Orders ◽  
Likelihood Ratio Order ◽  
Reliability Measures ◽  
Life Distributions ◽  
The Relationship ◽  
Double Truncation

The purpose of this paper is to study definitions and characterizations of orders based on reliability measures related with the doubly truncated random variable X[x, y] = (X|x ≤ X ≤ y). The relationship between these orderings and various existing orderings of life distributions are discussed. Moreover, we give two new characterizations of the likelihood ratio order based on double truncation. These new orders complete a general diagram between orders defined from truncation.

DERIVING ROBUST BAYESIAN PREMIUMS UNDER BANDS OF PRIOR DISTRIBUTIONS WITH APPLICATIONS

2018 ◽  
Vol 49 (1) ◽  
pp. 147-168 ◽  
Author(s):  
M. Sánchez-Sánchez ◽  
M.A. Sordo ◽  
A. Suárez-Llorens ◽  
E. Gómez-Déniz
Keyword(s):  
Bayesian Analysis ◽  
Likelihood Ratio ◽  
Requirements Elicitation ◽  
Likelihood Ratio Order ◽  
Prior Distributions ◽  
Propagation Of Uncertainty ◽  
Distortion Functions ◽  
Wide Family ◽  
Class Of Priors ◽  
Quantities Of Interest

AbstractWe study the propagation of uncertainty from a class of priors introduced by Arias-Nicolás et al. [(2016) Bayesian Analysis, 11(4), 1107–1136] to the premiums (both the collective and the Bayesian), for a wide family of premium principles (specifically, those that preserve the likelihood ratio order). The class under study reflects the prior uncertainty using distortion functions and fulfills some desirable requirements: elicitation is easy, the prior uncertainty can be measured by different metrics, and the range of quantities of interest is easily obtained from the extremal members of the class. We illustrate the methodology with several examples based on different claim counts models.

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