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

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.

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).

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.

Stochastic Orders Generated by Integrals: a Unified Study

1997 ◽  
Vol 29 (02) ◽  
pp. 414-428 ◽  
Author(s):  
Alfred Müller
Keyword(s):  
Functional Analysis ◽  
Weak Convergence ◽  
Likelihood Ratio ◽  
Stochastic Orders ◽  
Probability Measures ◽  
Likelihood Ratio Order ◽  
Unified Study ◽  
Maximal Cone ◽  
Class Of Functions

We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.

Stochastic Orders Generated by Integrals: a Unified Study

1997 ◽  
Vol 29 (2) ◽  
pp. 414-428 ◽  
Author(s):  
Alfred Müller
Keyword(s):  
Functional Analysis ◽  
Weak Convergence ◽  
Likelihood Ratio ◽  
Stochastic Orders ◽  
Probability Measures ◽  
Likelihood Ratio Order ◽  
Unified Study ◽  
Maximal Cone ◽  
Class Of Functions

We consider stochastic orders of the following type. Let be a class of functions and let P and Q be probability measures. Then define , if ∫ ⨍ d P ≦ ∫ ⨍ d Q for all f in . Marshall (1991) posed the problem of characterizing the maximal cone of functions generating such an ordering. We solve this problem by using methods from functional analysis. Another purpose of this paper is to derive properties of such integral stochastic orders from conditions satisfied by the generating class of functions. The results are illustrated by several examples. Moreover, we show that the likelihood ratio order is closed with respect to weak convergence, though it is not generated by integrals.

scholarly journals The Proportional Likelihood Ratio Order for Lindley Distribution

2011 ◽  
Vol 18 (4) ◽  
pp. 485-493 ◽  
Author(s):  
J. Jarrahiferiz ◽  
G.R. Mohtashami Borzadaran ◽  
A.H. Rezaei Roknabadi
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Order ◽  
Lindley Distribution
Sign in / Sign up

Export Citation Format

Share Document