Multivariate distributions characterized by a relationship between mean residual life and hazard rate

Metrika ◽  
1999 ◽  
Vol 49 (2) ◽  
pp. 121-126 ◽  
Author(s):  
Majid Asadi
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Multivariate Distributions

Dynamic multivariate mean residual life functions

1991 ◽  
Vol 28 (03) ◽  
pp. 613-629 ◽  
Author(s):  
Moshe Shaked ◽  
J. George Shanthikumar
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Stochastic Ordering ◽  
Partial Ordering ◽  
Mean Residual Life ◽  
Positive Dependence ◽  
Basic Properties ◽  
Rate Functions ◽  
Hazard Rate Ordering ◽  
Weak Notion

In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied. A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given. Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.

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.

MEAN RESIDUAL LIFE FUNCTION FOR ADDITIVE AND MULTIPLICATIVE HAZARD RATE MODELS

2015 ◽  
Vol 30 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Ramesh C. Gupta
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Turning Points ◽  
Sufficient Conditions ◽  
Mean Residual Life ◽  
Residual Life Function ◽  
Mean Residual Life Function ◽  
Hazard Rate Models ◽  
The Mean ◽  
Life Function

This paper deals with the mean residual life function (MRLF) and its monotonicity in the case of additive and multiplicative hazard rate models. It is shown that additive (multiplicative) hazard rate does not imply reduced (proportional) MRLF and vice versa. Necessary and sufficient conditions are obtained for the two models to hold simultaneously. In the case of non-monotonic failure rates, the location of the turning points of the MRLF is investigated in both the cases. The case of random additive and multiplicative hazard rate is also studied. The monotonicity of the mean residual life is studied along with the location of the turning points. Examples are provided to illustrate the results.

scholarly journals Estimation of Hazard Rate and Mean Residual Life Ordering for Fuzzy Random Variable

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
S. Ramasubramanian ◽  
P. Mahendran
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Mean Residual Life ◽  
Mean And Variance ◽  
The Mean ◽  
Hazard Rate Ordering ◽  
Fuzzy Random

L2-metric is used to find the distance between triangular fuzzy numbers. The mean and variance of a fuzzy random variable are also determined by this concept. The hazard rate is estimated and its relationship with mean residual life ordering of fuzzy random variable is investigated. Additionally, we have focused on deriving bivariate characterization of hazard rate ordering which explicitly involves pairwise interchange of two fuzzy random variablesXandY.

scholarly journals Sharp bounds for exponential approximations under a hazard rate upper bound

2015 ◽  
Vol 52 (03) ◽  
pp. 841-850 ◽  
Author(s):  
Mark Brown
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Residual Life ◽  
Continuous Distribution ◽  
Rate Function ◽  
Mean Residual Life ◽  
Birth And Death Processes ◽  
Absolutely Continuous ◽  
Sharp Bounds ◽  
Life Distributions

Consider an absolutely continuous distribution on [0, ∞) with finite meanμand hazard rate functionh(t) ≤bfor allt. Forbμclose to 1, we would expectFto be approximately exponential. In this paper we obtain sharp bounds for the Kolmogorov distance betweenFand an exponential distribution with meanμ, as well as betweenFand an exponential distribution with failure rateb. We apply these bounds to several examples. Applications are presented to geometric convolutions, birth and death processes, first-passage times, and to decreasing mean residual life distributions.

ON BOUNDS AND APPROXIMATING WEIGHTED DISTRIBUTIONS BY EXPONENTIAL DISTRIBUTIONS

2006 ◽  
Vol 20 (3) ◽  
pp. 517-528 ◽  
Author(s):  
Broderick O. Oluyede
Keyword(s):  
Error Bounds ◽  
Hazard Rate ◽  
Residual Life ◽  
Weight Functions ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Lifetime Distributions ◽  
Weighted Distributions

In this article, we obtain error bounds for exponential approximations to the classes of weighted residual and equilibrium lifetime distributions with monotone weight functions. These bounds are obtained for the class of distributions with increasing (decreasing) hazard rate and mean residual life functions.

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