scholarly journals Mean Residual Lifetime Frailty Models: A Weighted Perspective

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Mashael A. Alshehri ◽  
Mohamed Kayid
Keyword(s):  
Residual Life ◽  
Sufficient Conditions ◽  
Frailty Model ◽  
Random Parameter ◽  
Stochastic Orders ◽  
Residual Lifetime ◽  
Mean Residual Life ◽  
Aging Properties ◽  
Life Model ◽  
Multiplicative Mean

The mean residual life frailty model and a subsequent weighted multiplicative mean residual life model that requires weighted multiplicative mean residual lives are considered. The expression and the shape of a mean residual life for some semiparametric models and also for a multiplicative degradation model are given in separate examples. The frailty model represents the lifetime of the population in which the random parameter combines the effects of the subpopulations. We show that for some regular dependencies of the population lifetime on the random parameter, some aging properties of the subpopulations’ lifetimes are preserved for the population lifetime. We indicate that the weighted multiplicative mean residual life model generates positive dependencies of this type. The copula function associated with the model is also derived. Necessary and sufficient conditions for certain aging properties of population lifetimes in the model are determined. Preservation of stochastic orders of two random parameters for the resulting population lifetimes in the model is acquired.

An additive-multiplicative mean residual life model for right-censored data

2017 ◽  
Vol 59 (3) ◽  
pp. 579-592 ◽  
Author(s):  
Jingheng Cai ◽  
Haijin He ◽  
Xinyuan Song ◽  
Liuquan Sun
Keyword(s):  
Censored Data ◽  
Residual Life ◽  
Mean Residual Life ◽  
Right Censored Data ◽  
Life Model ◽  
Multiplicative Mean

ON DYNAMIC PROPORTIONAL MEAN RESIDUAL LIFE MODEL

2013 ◽  
Vol 27 (4) ◽  
pp. 553-588 ◽  
Author(s):  
Asok K. Nanda ◽  
Suchismita Das ◽  
N. Balakrishnan
Keyword(s):  
Residual Life ◽  
Stochastic Orders ◽  
Mean Residual Life ◽  
Life Model

Recently, proportional mean residual life model has received a lot of attention after the importance of the model was discussed by Zahedi [17]. In this paper, we define dynamic proportional mean residual life model and study its properties for different aging classes. The closure of this model under different stochastic orders is also discussed. Many examples are presented to illustrate different properties of the model.

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.

Random Effect Additive Mean Residual Life Model

2016 ◽  
Vol 65 (2) ◽  
pp. 860-866 ◽  
Author(s):  
M. Kayid ◽  
S. Izadkhah ◽  
D. ALmufarrej
Keyword(s):  
Residual Life ◽  
Random Effect ◽  
Mean Residual Life ◽  
Life Model

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.

On the Mixture Proportional Mean Residual Life Model

2013 ◽  
Vol 44 (20) ◽  
pp. 4263-4277 ◽  
Author(s):  
Majid Rezaei ◽  
Behzad Gholizadeh
Keyword(s):  
Residual Life ◽  
Mean Residual Life ◽  
Life Model

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.

A GENERALIZED ENTROPY-BASED RESIDUAL LIFETIME DISTRIBUTIONS

2011 ◽  
Vol 04 (02) ◽  
pp. 171-184 ◽  
Author(s):  
VIKAS KUMAR ◽  
H. C. TANEJA
Keyword(s):  
Residual Life ◽  
Survival Function ◽  
Monotonicity Property ◽  
Entropy Measure ◽  
Residual Lifetime ◽  
Mean Residual Life ◽  
Present Communication ◽  
Dynamic Information ◽  
Lifetime Distributions ◽  
Life Function

The present communication considers Havrda and Charvat entropy measure to propose a generalized dynamic information measure. It is shown that the proposed measure determines the survival function uniquely. The residual lifetime distributions have been characterized. A bound for the dynamic entropy measure in terms of mean residual life function has been derived, and its monotonicity property is studied.

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