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.

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.

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

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

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

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.

scholarly journals Fisher consistent estimation of regression parameter in the proportional mean residual life model with frailty

Ekonomia ◽  
2021 ◽  
Vol 27 (2) ◽  
pp. 81-88
Author(s):  
Magdalena Skolimowska-Kulig
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Regression Models ◽  
Residual Life ◽  
Likelihood Estimation ◽  
Mean Residual Life ◽  
Regression Parameter ◽  
Consistent Estimation ◽  
Regression Parameters ◽  
Life Model

In the article, we consider the Fisher consistent estimation of the regression parameters in the proportional mean residual life model with arbitrary frailty. It is discussed that conventional estimation procedures, such as the maximum likelihood estimation or Cox’s approach, which are employed in common regression models, may also yield consistent inference in the extended models.

scholarly journals Rank Estimation for Mean Residual Life Transformation Model

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xiaoping Chen
Keyword(s):  
Residual Life ◽  
Rank Correlation ◽  
Transformation Model ◽  
Mean Residual Life ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Life Model ◽  
The Mean ◽  
Life Transformation

This paper proposes a new and important class of mean residual life regression model, which is called the mean residual life transformation model.  The link function is assumed to be unknown and increasing in its second argument, but it is permitted to be not differentiable. The mean residual life transformation model encompasses the proportional mean residual life model, the additive mean residual life model, and so on. Under maximum rank correlation estimation, we present the estimation procedures, whose asymptotic and finite sample properties are established. The consistent variance can be estimated by a resampling method via perturbing the U -statistics objective function repeatedly which avoids the usual sandwich choice. Monte Carlo simulations reveal good finite sample performance and the estimators are illustrated with the Oscar data set.

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