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.

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.

Some Characterizations of a Multivariate Lomax Distribution Within the Class of Generalised Mixtures of Exponential Distributions

1997 ◽  
Vol 47 (1-2) ◽  
pp. 11-21 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Hazard Rate ◽  
Residual Life ◽  
Mean Residual Life ◽  
Exponential Distributions ◽  
Closure Properties ◽  
Lomax Distribution ◽  
Selection Of ◽  
Multivariate Lomax Distribution

Selection of the Lomax model through characterization results from amongst the class of continuous mixtures of exponential distributions has been examined. Properties covered are in main based on crude measures of hazard rate and mean residual life. Some closure properties have also been used for this purpose.

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.

On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (02) ◽  
pp. 574-576
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

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.

RELIABILITY PROPERTIES OF MEAN TIME TO FAILURE IN AGE REPLACEMENT MODELS

2010 ◽  
Vol 17 (01) ◽  
pp. 15-26 ◽  
Author(s):  
G. ASHA ◽  
N. UNNIKRISHNAN NAIR
Keyword(s):  
Residual Life ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Time To Failure ◽  
Mean Time To Failure ◽  
Replacement Model ◽  
The Mean ◽  
Age Replacement ◽  
The Relationship ◽  
Mean Time

In this article some properties of the mean time to failure in an age replacement model is presented by examining the relationship it has with hazard (reversed hazard) rate and mean (reversed mean) residual life functions. An ordering based on mean time to failure is used to examine its implications with other stochastic orders.

On a characterization of gamma distributions via exponential mixtures

1980 ◽  
Vol 17 (2) ◽  
pp. 574-576 ◽  
Author(s):  
Manish C. Bhattacharjee
Keyword(s):  
General Result ◽  
Residual Life ◽  
Infinite Divisibility ◽  
Mean Residual Life ◽  
Gamma Distributions ◽  
Mixing Distributions

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

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