scholarly journals On hazard rate ordering of dependent variables

1993 ◽  
Vol 25 (2) ◽  
pp. 477-482 ◽  
Author(s):  
Emad-Eldin A. A. Aly ◽  
Subhash C. Kochar
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Scale Model ◽  
Stochastic Orders ◽  
Marginal Distributions ◽  
New Concepts ◽  
Dependent Variables ◽  
Likelihood Ratio Ordering ◽  
Hazard Rate Ordering ◽  
Stochastic Order Relations

Shanthikumar and Yao (1991) introduced some new stochastic order relations to compare the components of a bivariate random vector (X1, X2). As they point out in their paper, even if according to their hazard rate (or likelihood ratio) ordering, the marginal distributions may not be ordered accordingly. We introduce some new concepts where the marginal distributions preserve the corresponding stochastic orders. Also a relation between the bivariate scale model and the introduced bivariate hazard rate ordering is established.

scholarly journals On hazard rate ordering of dependent variables

1993 ◽  
Vol 25 (02) ◽  
pp. 477-482 ◽  
Author(s):  
Emad-Eldin A. A. Aly ◽  
Subhash C. Kochar
Keyword(s):  
Hazard Rate ◽  
Stochastic Order ◽  
Scale Model ◽  
Stochastic Orders ◽  
Marginal Distributions ◽  
New Concepts ◽  
Dependent Variables ◽  
Likelihood Ratio Ordering ◽  
Hazard Rate Ordering ◽  
Stochastic Order Relations

Shanthikumar and Yao (1991) introduced some new stochastic order relations to compare the components of a bivariate random vector (X 1, X 2). As they point out in their paper, even if according to their hazard rate (or likelihood ratio) ordering, the marginal distributions may not be ordered accordingly. We introduce some new concepts where the marginal distributions preserve the corresponding stochastic orders. Also a relation between the bivariate scale model and the introduced bivariate hazard rate ordering is established.

scholarly journals DEPENDENCE, DISPERSIVENESS, AND MULTIVARIATE HAZARD RATE ORDERING

2005 ◽  
Vol 19 (4) ◽  
pp. 427-446 ◽  
Author(s):  
Baha-Eldin Khaledi ◽  
Subhash Kochar
Keyword(s):  
Multivariate Analysis ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Random Vectors ◽  
Positive Dependence ◽  
Marginal Distributions ◽  
Dispersive Ordering ◽  
Hazard Rate Ordering

To compare two multivariate random vectors of the same dimension, we define a new stochastic order called upper orthant dispersive ordering and study its properties. We study its relationship with positive dependence and multivariate hazard rate ordering as defined by Hu, Khaledi, and Shaked (Journal of Multivariate Analysis, 2002). It is shown that if two random vectors have a common copula and if their marginal distributions are ordered according to dispersive ordering in the same direction, then the two random vectors are ordered according to this new upper orthant dispersive ordering. Also, it is shown that the marginal distributions of two upper orthant dispersive ordered random vectors are also dispersive ordered. Examples and applications are given.

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.

PRESERVATION OF STOCHASTIC ORDERS UNDER MIXTURES OF EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (4) ◽  
pp. 655-666 ◽  
Author(s):  
Jarosław Bartoszewicz ◽  
Magdalena Skolimowska
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Order ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Dispersive Order ◽  
Mixing Distributions ◽  
Convex Transform Order ◽  
Star Order

Recently, Bartoszewicz [5,6] considered mixtures of exponential distributions treated as the Laplace transforms of mixing distributions and established some stochastic order relations between them: star order, dispersive order, dilation. In this article the preservation of the likelihood ratio, hazard rate, reversed hazard rate, mean residual life, and excess wealth orders under exponential mixtures is studied. Some new preservation results for the dispersive order are given, as well as the preservation of the convex transform order, and the star one is discussed.

ORDERING PROPERTIES OF EXTREME CLAIM AMOUNTS FROM HETEROGENEOUS PORTFOLIOS

2019 ◽  
Vol 49 (2) ◽  
pp. 525-554 ◽  
Author(s):  
Yiying Zhang ◽  
Xiong Cai ◽  
Peng Zhao
Keyword(s):  
Sufficient Conditions ◽  
Stochastic Ordering ◽  
Stochastic Orders ◽  
Reliability Engineering ◽  
Research Fields ◽  
Likelihood Ratio Ordering ◽  
Hazard Rate Ordering ◽  
Arrangement Increasing ◽  
The Right ◽  
Stochastic Properties

AbstractIn the context of insurance, the smallest and largest claim amounts turn out to be crucial to insurance analysis since they provide useful information for determining annual premium. In this paper, we establish sufficient conditions for comparing extreme claim amounts arising from two sets of heterogeneous insurance portfolios according to various stochastic orders. It is firstly shown that the weak supermajorization order between the transformed vectors of occurrence probabilities implies the usual stochastic ordering between the largest claim amounts when the claim severities are weakly stochastic arrangement increasing. Secondly, sufficient conditions are established for the right-spread ordering and the convex transform ordering of the smallest claim amounts arising from heterogeneous dependent insurance portfolios with possibly different number of claims. In the setting of independent multiple-outlier claims, we study the effects of heterogeneity among sample sizes on the stochastic properties of the largest and smallest claim amounts in the sense of the hazard rate ordering and the likelihood ratio ordering. Numerical examples are provided to highlight these theoretical results as well. Not only can our results be applied in the area of actuarial science, but also they can be used in other research fields including reliability engineering and auction theory.

On allocation of spares at component level versus system level

1997 ◽  
Vol 34 (01) ◽  
pp. 283-287 ◽  
Author(s):  
Harshinder Singh ◽  
R. S. Singh
Keyword(s):  
Survival Analysis ◽  
Hazard Rate ◽  
System Level ◽  
Component Level ◽  
Design Engineers ◽  
Versus System ◽  
Level Versus ◽  
Life Distributions ◽  
Likelihood Ratio Ordering ◽  
Hazard Rate Ordering

Design engineers are well aware that a system where active spare allocation is made at the component level has a lifetime stochastically larger than the corresponding system where active spare allocation is made at the system level. In view of the importance of hazard rate ordering in reliability and survival analysis, Boland and El-Neweihi (1995) recently investigated this principle in hazard rate ordering and demonstrated that it does not hold in general. They showed that for a 2-out-of-n system with independent and identical components and spares, active spare allocation at the component level is superior to active spare allocation at the system level. They conjectured that such a principle holds in general for a k-out-of-n system when components and spares are independent and identical. We prove that for a k-out-of-n system where components and spares have independent and identical life distributions active spare allocation at the component level is superior to active spare allocation at the system level in likelihood ratio ordering. This is stronger than hazard rate ordering, thus establishing the conjecture of Boland and El-Neweihi (1995).

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.

Order-Preserving Shock Models

1994 ◽  
Vol 8 (1) ◽  
pp. 125-134 ◽  
Author(s):  
Y. Kebir
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Ordering ◽  
Shock Models ◽  
Likelihood Ratio Ordering ◽  
Hazard Rate Ordering

To date, research in shock models has been primarily concerned with the classpreserving properties of certain shock and damage kernels. This article focuses on the order-preserving properties of those kernels. We show that they preserve stochastic ordering, hazard rate ordering, backward hazard rate ordering, and likelihood ratio ordering.

Bivariate characterization of some stochastic order relations

1991 ◽  
Vol 23 (3) ◽  
pp. 642-659 ◽  
Author(s):  
J. George Shanthikumar ◽  
David D. Yao
Keyword(s):  
Stochastic Order ◽  
Queueing Network ◽  
Stochastic Scheduling ◽  
Stochastic Ordering ◽  
Closed Queueing Network ◽  
Order Relations ◽  
Functional Representations ◽  
Hazard Rate Ordering ◽  
Stochastic Order Relations

Bivariate (and multivariate) functional representations for the following stochastic order relations are established: the likelihood ratio ordering, hazard rate ordering, and the usual stochastic ordering. The motivation of the study is (i) to provide a general approach that supports the ‘pairwise interchange' arguments widely used in various settings, and (ii) to develop new notions of stochastic order relations so that dependent random variables can be meaningfully compared. Applications are illustrated through problems in stochastic scheduling, closed queueing network and reliability.

ORDERING RESULTS ON EXTREMES OF EXPONENTIATED LOCATION-SCALE MODELS

2019 ◽  
pp. 1-24
Author(s):  
Sangita Das ◽  
Suchandan Kayal ◽  
Debajyoti Choudhuri
Keyword(s):  
Likelihood Ratio ◽  
Hazard Rate ◽  
Stochastic Order ◽  
Scale Model ◽  
Likelihood Ratio Order ◽  
Hazard Rate Order ◽  
Number Of Components ◽  
Usual Stochastic Order ◽  
Scale Models ◽  
Unequal Number

AbstractIn this paper, we consider exponentiated location-scale model and obtain several ordering results between extreme order statistics in various senses. Under majorization type partial order-based conditions, the comparisons are established according to the usual stochastic order, hazard rate order and reversed hazard rate order. Multiple-outlier models are considered. When the number of components are equal, the results are obtained based on the ageing faster order in terms of the hazard rate and likelihood ratio orders. For unequal number of components, we develop comparisons according to the usual stochastic order, hazard rate order, and likelihood ratio order. Numerical examples are considered to illustrate the results.

Sign in / Sign up

Export Citation Format

Share Document