A Multivariate Weibull Distribution

Lee, Cheng K.; Wen, Miin-Jye

doi:10.18187/pjsor.v5i2.120

Cited by 18 publications

(12 citation statements)

References 23 publications

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“…The joint survival function for the trivariate Weibull distribution of random variable T 1 , T 2 and T 3 proposed by Lee and Wen (2009) for 0 < α ≤ 1; 0 ≤ t 1 , t 2 , t 3 < ∞ is given by Eq. 3:…”

Section: Methodsmentioning

confidence: 99%

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The Development of Parameter Estimation on Hazard Rate of Trivariate Weibull Distribution

Wahyudi¹,

Purhadi²,

Irhamah³

et al. 2012

American Journal of Biostatistics

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In this study, the interrelation concepts of trivariate distribution function, trivariate survival function, trivariate probability density function and trivariate hazard rate function of trivariate Weibull distribution are presented. The goal of this contribution is to estimate the trivariate Weibull hazard rate parameters. To reach this goal, we will use an analitical approach in estimating called the Maximum Likelihood Estimation (MLE) method. Using numerical iterative procedure the scale parameters, the shape parameters and the power parameter estimators on trivariate hazard rate of trivariate Weibull distribution must be obtained. The MLE technique estimates accurately the trivariate Weibull hazard rate parameters.

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Section: Methodsmentioning

confidence: 99%

“…Lee and Wen (2009) propose a multivariate Weibull model and derived the explicit form of PDF, CDF and general moment.…”

Section: Introductionmentioning

confidence: 99%

The Development of Parameter Estimation on Hazard Rate of Trivariate Weibull Distribution

Wahyudi¹,

Purhadi²,

Irhamah³

et al. 2012

American Journal of Biostatistics

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“…Maximum likelihood (ML) approach . ML is a common approach for parameter estimation; its state of the art for bivariate distribution is firstly to build up the likelihood function . Suppose the density function of bivariate distribution is f ( x , y ; α 1 , β 1 , α 2 , β 2 , γ ).…”

Section: Literature Surveymentioning

confidence: 99%

“…There are a few publications found in the state of the art for bivariate distribution using the moment method. Lee and Wen uses the special property of the bivariate Weibull distribution to derive a moment method. However, the bivariate Weibull model addressed in Lee and Wen differs from the model this paper addresses.…”

Section: Literature Surveymentioning

confidence: 99%

Parameter estimation for bivariate Weibull distribution using generalized moment method for reliability evaluation

Yuan

2018

Quality & Reliability Eng

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Bivariate Weibull distribution can address the life of a system exhibiting 2‐dimensional characteristics in risk and reliability engineering. The applicability of bivariate Weibull distribution has been hindered by its difficulty with parameter estimation, as the number of parameters in bivariate Weibull distribution is more than those in univariate Weibull distribution. Considering a particular structure of a bivariate Weibull distribution model, this paper proposes a generalized moment method (GMM) for parameter estimation. This GMM method is simple, and it has proved to be efficient. The GMM can guarantee the existence and the uniqueness of the solution. A confidence interval for each estimator is derived from the moments of the bivariate distribution. The paper presents a simulation case and 2 real cases to demonstrate the proposed methods.

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“…. , Lee and Wen (2010) derive the density and the general moments of the distribution for any integer k ≥ 2. They also apply the model to a data set with three variables.…”

Section: Other Competing Risks Modelsmentioning

confidence: 99%

Characteristics of two Competing Risks Models with Weibull Distributed Risks

Yáñez

Escobar

González

2014

Rev. Acad. Colomb. Cienc. Ex. Fis. Nat.

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Lifetime and survival data are usually the lives of subjects, units, or systems that has been exposed to multiple risks or modes of failure. In the analysis of the data, however, is common to ignore the modes of failure because they are unknown, they are not recorded, or because the complexity of including them in the modeling. It is of interest knowing when the conclusions might be robust to ignoring the failure modes in the analysis. In particular, it would be useful to characterize situations where it could be safely said that the modes of failure effect on the analysis would be negligible or that failing to include such information could completely invalidate the conclusions drawn from the study. As a first step in identifying when the failure modes have little or large influence on the competing risks model, this article studies two different competing risks models: (a) a model with independent risks; (b) a model derived from a multivariate Weibull with dependence.Key words: competing risks, probability plots, log-location-scale family, Weibull distribution, multivariate Weibull with dependence, lognormal distribution. Caracteristicas de dos modelos con riesgos en competencia y riesgos Weibull. ResumenLos datos de tiempos de falla y sobrevivencia se refieren generalmente a la vida de individuos, unidades o sistemas que han sido expuestos a múltiples riesgos o modos de falla. Sin embargo, en el análisis de los datos es común ignorar los modos de falla porque son desconocidos, no se registran o por la complejidad de la modelación al incluirlos. Es importante, por lo tanto, determinar la robustez del análisis ignorando los modos de falla. En particular, sería útil caracterizar situaciones donde pudiera decirse que el efecto de los modos de falla en el análisis es despreciable o donde no incluir tal información pudiera invalidar completamente las inferencias del estudio. Como un primer paso para identificar cuando los modos de falla tienen poca o mucha influencia en el modelo de riesgos en competencia, este artículo estudia dos modelos de riesgos en competencia: (a) un modelo con riesgos independientes; (b) un modelo derivado de una distribución Weibull multivariada con dependencia.Palabras clave: riesgos en competencia, gráficos de probabilidad, familia de log-localización y escala, distribución Weibull, distribución Weibull multivariada con dependencia, distribución lognormal.

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A Multivariate Weibull Distribution

Cited by 18 publications

References 23 publications

The Development of Parameter Estimation on Hazard Rate of Trivariate Weibull Distribution

The Development of Parameter Estimation on Hazard Rate of Trivariate Weibull Distribution

Parameter estimation for bivariate Weibull distribution using generalized moment method for reliability evaluation

Characteristics of two Competing Risks Models with Weibull Distributed Risks

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