Log-location-scale-log-concave distributions for survival and reliability analysis

Jones, M. C.; Noufaily, Angela

doi:10.1214/15-ejs1089

Cited by 13 publications

(11 citation statements)

References 23 publications

(29 reference statements)

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“…It can be shown that the APGW distribution retains membership of the log‐location–scale–log‐concave family of distributions of Jones and Noufaily () and therefore, inter alia , unimodality of densities. We also now note, for future reference, the attractive form of the quantile function that is associated with H A , namely, Q A ( u )=[ H A {− log (1− u );1,1/ κ }] 1/ γ ≡ Q A1 ( u ; κ ) 1/ γ .…”

Section: The Specific Model For H0mentioning

confidence: 99%

“…Note that the Gompertz hazard function, h A .t; γ = 1, κ = ∞/ = exp.t/, including both vertical and horizontal scaling parameters, is λφ exp.φt/, and this can be reparameterized as λ Å exp.φt/ to arrive at the familiar form due to Gompertz (1825); see the on-line supplementary material for more Gompertz-related discussion. It can be shown that the APGW distribution retains membership of the log-location-scalelog-concave family of distributions of Jones and Noufaily (2015) and therefore, inter alia, unimodality of densities. We also now note, for future reference, the attractive form of the quantile function that is associated with H A , namely,…”

Section: Basic Definition and Propertiesmentioning

confidence: 99%

“…Both the PGW and the APGW distributions share the set of hazard behaviours that are listed in Table 1 with two other established two-shape-parameter lifetime distributions centred on the Weibull distribution, namely, the generalized gamma (GG) and exponentiated Weibull (EW) distributions; see Jones and Noufaily (2015). Indeed, Rubio et al (2019) chose to perform parametric survival analysis by using the EW distribution for this reason.…”

Section: Why This Particular Choice For H 0 ?mentioning

confidence: 99%

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A Flexible Parametric Modelling Framework for Survival Analysis

Burke

Jones

Noufaily

2020

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard functions (constant; increasing; decreasing; up then down; down then up) and various common survival distributions (log‐logistic; Burr type XII; Weibull; Gompertz) and includes defective distributions (cure models). This generality is achieved by using four distributional parameters: two scale‐type parameters—one of which relates to accelerated failure time (AFT) modelling; the other to proportional hazards (PH) modelling—and two shape parameters. Furthermore, we advocate ‘multiparameter regression’ whereby more than one distributional parameter depends on covariates—rather than the usual convention of having a single covariate‐dependent (scale) parameter. This general formulation unifies the most popular survival models, enabling us to consider the practical value of possible modelling choices. In particular, we suggest introducing covariates through just one or other of the two scale parameters (covering AFT and PH models), and through a ‘power’ shape parameter (covering more complex non‐AFT or non‐PH effects); the other shape parameter remains covariate independent and handles automatic selection of the baseline distribution. We explore inferential issues and compare with alternative models through various simulation studies, with particular focus on evidence concerning the need, or otherwise, to include both AFT and PH parameters. We illustrate the efficacy of our modelling framework by using data from lung cancer, melanoma and kidney function studies. Censoring is accommodated throughout.

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Section: The Specific Model For H0mentioning

confidence: 99%

Section: Basic Definition and Propertiesmentioning

confidence: 99%

Section: Why This Particular Choice For H 0 ?mentioning

confidence: 99%

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A Flexible Parametric Modelling Framework for Survival Analysis

Burke

Jones

Noufaily

2020

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…Transforming the location-scale distribution using X = log(Y ) in which Y = e x produces a log-location-scale distribution. Based on this transformation, the location parameter µ becomes θ = e µ and the scale parameter σ becomes λ = 1/σ where θ is called the scale parameter and λ is called the power parameter [71].…”

Section: Location-scale and Log Location-scale Distributionmentioning

confidence: 99%

Prognostics and Health Monitoring Methodologies and Approaches: A Review

Bjaili

Rushdi

2020

JERR

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Prognostics is a term that engineering borrowed from medicine to refer to the discipline concerned with the Remaining Useful Life (RUL) of an engineering device. This paper surveys the RUL prediction techniques and classifies them into four categories of model-based techniques,knowledge-based techniques, experience-based techniques, and data-driven techniques. A comparative review is given for the main features, prominent advantages, potential shortcomings and main subcategories for each of these categories. The survey is supported by an extensive listfor up-to-date references.

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“…The PGW distribution was first introduced by Bagdonaviçius and Nikulin 7 (see also Nikulin and Haghighi 8 ), independently re-introduced by Dimitrakopoulou et al., 9 and recognized as an interesting competitor to the GG and EW distributions in Jones and Noufaily. 10…”

Section: Univariate Backgroundmentioning

confidence: 99%

A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

Jones

Noufaily

Burke

2019

Stat Methods Med Res

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We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we have extolled the virtues of the "power generalized Weibull" (PGW) distribution as an attractive vehicle for univariate parametric survival analysis: it is a tractable, parsimonious, model which interpretably allows for a wide variety of hazard shapes and, when adapted (to give an adapted PGW, or APGW, distribution), covers a wide variety of important special/limiting cases. Here, we additionally observe a frailty relationship between a PGW distribution with one value of the parameter which controls distributional choice within the family and a PGW distribution with a smaller value of the same parameter. We exploit this frailty relationship to propose a bivariate shared frailty model with PGW marginal distributions: these marginals turn out to be linked by the so-called BB9 or "power variance function" copula. This particular choice of copula is, therefore, a natural one in the current context. We then adapt the bivariate PGW distribution, in turn, to accommodate APGW marginals. We provide a number of theoretical properties of the bivariate PGW and APGW models and show the potential of the latter for practical work via an illustrative example involving a well-known retinopathy dataset, for which the analysis proves to be straightforward to implement and informative in its outcomes. The novelty in this article is in the appropriate combination of specific ingredients into a coherent and successful whole.

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Log-location-scale-log-concave distributions for survival and reliability analysis

Cited by 13 publications

References 23 publications

A Flexible Parametric Modelling Framework for Survival Analysis

A Flexible Parametric Modelling Framework for Survival Analysis

Prognostics and Health Monitoring Methodologies and Approaches: A Review

A bivariate power generalized Weibull distribution: A flexible parametric model for survival analysis

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