scholarly journals Multivariate Likelihood Ratio Order for Skew-Symmetric Distributions with a Common Kernel

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Werner Hürlimann
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Symmetric Distributions ◽  
Invariance Properties ◽  
Multivariate Likelihood ◽  
Perturbation Invariance ◽  
Order Comparison

The multivariate likelihood ratio order comparison of skew-symmetric distributions with a common kernel is considered. Two multivariate likelihood ratio perturbation invariance properties are derived.

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.

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.

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.

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).

Likelihood ratio order of the second spacing in multiple-outlier exponential models

Statistics ◽  
2015 ◽  
Vol 50 (1) ◽  
pp. 206-218
Author(s):  
Peng Zhao ◽  
Jianfei Qiao ◽  
N. Balakrishnan
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Exponential Models

APPLICATIONS OF LIKELIHOOD RATIO ORDER IN BAYESIAN INFERENCES

2018 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kai Huang ◽  
Jie Mi
Keyword(s):  
Likelihood Ratio ◽  
Bayes Factor ◽  
Loss Functions ◽  
Posterior Distributions ◽  
Likelihood Ratio Order ◽  
Predictive Distributions ◽  
Sufficient Statistic ◽  
Bayesian Inferences ◽  
Bayesian Estimators ◽  
General Error

The present paper studies the likelihood ratio order of posterior distributions of parameter when the same order exists between the corresponding prior of the parameter, or when the observed values of the sufficient statistic for the parameter differ. The established likelihood order allows one to compare the Bayesian estimators associated with many common and general error loss functions analytically. It can also enable one to compare the Bayes factor in hypothesis testing without using numerical computation. Moreover, using the likelihood ratio (LR) order of the posterior distributions can yield the LR order between marginal predictive distributions, and posterior predictive distributions.

STOCHASTIC MONOTONICITY OF CONDITIONAL ORDER STATISTICS IN MULTIPLE-OUTLIER SCALE POPULATION

2016 ◽  
Vol 31 (3) ◽  
pp. 366-380
Author(s):  
Ebrahim Amini-Seresht ◽  
Yiying Zhang
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Likelihood Ratio ◽  
Monotonicity Property ◽  
Independent Random Variables ◽  
Likelihood Ratio Order ◽  
Stochastic Monotonicity ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Parametric Families

This paper discusses the stochastic monotonicity property of the conditional order statistics from independent multiple-outlier scale variables in terms of the likelihood ratio order. Let X1, …, Xn be a set of non-negative independent random variables with Xi, i=1, …, p, having common distribution function F(λ1x), and Xj, j=p+1, …, n, having common distribution function F(λ2x), where F(·) denotes the baseline distribution. Let Xi:n(p, q) be the ith smallest order statistics from this sample. Denote by $X_{i,n}^{s}(p,q)\doteq [X_{i:n}(p,q)|X_{i-1:n}(p,q)=s]$. Under the assumptions that xf′(x)/f(x) is decreasing in x∈ℛ+, λ1≤λ2 and s1≤s2, it is shown that $X_{i:n}^{s_{1}}(p+k,q-k)$ is larger than $X_{i:n}^{s_{2}}(p,q)$ according to the likelihood ratio order for any 2≤i≤n and k=1, 2, …, q. Some parametric families of distributions are also provided to illustrate the theoretical results.

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