Stochastic properties of a weighted frailty model

Jarrahiferiz, Jalil; Kayid, Mohamed; Izadkhah, S.

doi:10.1007/s00362-016-0826-z

Cited by 8 publications

(6 citation statements)

References 28 publications

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“…V (1) (t) − V (3) (t) V (1) We can conclude that (V ′ (t)/V ′ (0))λ(θ * )e − (V(t)/θ * ) is TP 2 in (t, θ * ) since, for all t ≥ 0 and for all θ * > 0,…”

mentioning

confidence: 86%

“…e goal of the current investigation is to consider a general mean residual lifetime frailty model and a particular weighted PMRL model. is model is raised by adding a multiplicative external parameter to the family of distributions generated by (3). is provides the possibility of external effects, separate from the variation of time-dependent coefficientB(t), to be entertained by the new model.…”

Section: Theorem 1 If E(t * ) < ∞ Then the Population-level Mrlf Is The Expectation Of M(t|θ) With Regard To The Conditional Density Of θmentioning

confidence: 99%

“…For instance, in the Cox PH model, h(t|Z) � e β T (t)Z h 0 (t) in which h 0 (t) is the baseline HRF, β(t) is a p-varaite vector of external parameters and Z is the p-dimensional vector of covariates. To develop the PH model to entertain mutual effect of time and covariates, Jarrahiferiz et al [3] proposed the weighted PH model as in (2). In a similar manner, a weighted version of the PMRL model can be defined.…”

Section: Weighted Multiplicative Mean Residual Life Modelmentioning

confidence: 99%

“…As conclusion, they showed that certain monotonicity properties of the function b(t) generate specific stochastic characteristics of the model that may contribute for inferential purposes and model selection strategies. Jarrahiferiz et al [3] added a parameter to the family of distributions given rise to (1) to obtain a model with HRF h(t|θ) � θb(t)h 0 (t).…”

Section: Introductionmentioning

confidence: 99%

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Mean Residual Lifetime Frailty Models: A Weighted Perspective

Alshehri

Kayid

2021

Mathematical Problems in Engineering

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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.

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“…V (1) (t) − V (3) (t) V (1) We can conclude that (V ′ (t)/V ′ (0))λ(θ * )e − (V(t)/θ * ) is TP 2 in (t, θ * ) since, for all t ≥ 0 and for all θ * > 0,…”

mentioning

confidence: 86%

Section: Theorem 1 If E(t * ) < ∞ Then the Population-level Mrlf Is The Expectation Of M(t|θ) With Regard To The Conditional Density Of θmentioning

confidence: 99%

Section: Weighted Multiplicative Mean Residual Life Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mean Residual Lifetime Frailty Models: A Weighted Perspective

Alshehri

Kayid

2021

Mathematical Problems in Engineering

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“…In this section, sufficient conditions to get the closure property of the PMDT model with respect to the reversed hazard rate (mean inactivity time) order and also sufficient conditions to establish the closure property of the model with respect to four reliability classes related to the inactivity time will be presented. Closure properties of models in reliability and survival analysis have attracted the attention of many researchers in the recent past decades (see, e.g., Crescenzo [22], Abouammoh and Qamber [23], Nanda et al [24], Nanda and Das [25], Kayid et al [26], and Jarrahiferiz et al [27] among others). Below the definition of three stochastic orders are given (see Shaked and Shanthikumar [28] and Ahmad and Kayid [29]).…”

Section: Closure Properties With Respect To Some Reliability Classes ...mentioning

confidence: 99%

Reliability Analysis of the Proportional Mean Departure Time Model

Shrahili

Kayid

2022

Journal of Mathematics

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In this article, the mean lifetime of an individual whose lives lost based on a function of the time before which the individual has passed away is considered. The measure is used to construct a semi-parametric model called proportional mean departure time model. Examples are given and evidences are gathered to show that the model is a proper alternative for the proportional mean past lifetime model. Closure properties of the model concerning several stochastic orders and a number of reliability properties are established. Finally, the model is extended to entertain random amounts of the parameter and establish a proportional mean departure time frailty model. Further stochastic properties using several stochastic orders are developed in the context of the frailty model.

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On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures

Badía

Lee

2019

Metrika

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Stochastic properties of a weighted frailty model

Cited by 8 publications

References 28 publications

Mean Residual Lifetime Frailty Models: A Weighted Perspective

Mean Residual Lifetime Frailty Models: A Weighted Perspective

Reliability Analysis of the Proportional Mean Departure Time Model

On stochastic comparisons and ageing properties of multivariate proportional hazard rate mixtures

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