Some Inference Results in Modified Freund's Bivariate Exponential Distribution

Hanagal, David D.

doi:10.1002/bimj.4710340615

Cited by 31 publications

(16 citation statements)

References 6 publications

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“…For the bivariate lifetime distribution, we use univariate censoring scheme given by Hanagal (1992aHanagal ( , 1992b) because individuals do not enter at the same time and withdrawal or death of an individual or termination of the study will censor both lifetimes of the components. Here the censoring time is independent of the lifetimes of both components.…”

Section: Parameter Estimation Of Marshall-olkin Methodsmentioning

confidence: 99%

“…(1) To generate values for parameters, a candidate function is needed, therefore we used the following consistent estimators, modified version suggested by Hanagal (1992b):…”

Section: Mcmc Methodsmentioning

confidence: 99%

“…Hanagal (1992aHanagal ( , 1992b have obtained maximum-likelihood estimations (MLEs) of the parameters when univariate right censoring is taken into account. Pena and Gupta (1990) obtained Bayesian estimation of parameters for Marshall-Olkin bivariate exponential distribution (BVED) when no censoring happened.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

Angali

Latifi

Hanagal

2013

Communications in Statistics - Simulation and Computation

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In this article, four bivariate exponential (BVE) distributions with subject to right censoring samples are presented. Bayesian estimates of the parameters of BVE are obtained through Linex and quadratic loss functions. Gamma prior distribution has been suggested to reforming the posterior function. The estimations and standard errors of parameters have also been obtained through simulation method. Markov chain Monte Carlo (MCMC) method is employed for the case of Block-Buse bivariate distribution because there was no closed form for estimator criteria. Simulation studies have been conducted to show that the computation parts can be implemented easily and comparing the estimated values due to two methods and with the true values as well.

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Section: Parameter Estimation Of Marshall-olkin Methodsmentioning

confidence: 99%

“…(1) To generate values for parameters, a candidate function is needed, therefore we used the following consistent estimators, modified version suggested by Hanagal (1992b):…”

Section: Mcmc Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

Angali

Latifi

Hanagal

2013

Communications in Statistics - Simulation and Computation

Self Cite

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“…Hence it is interesting to follow independency test. In order to confirm that there is dependence between paired eyes, the hypotheses is put in the form Hanagal (1992b) and Hanagal and Kale (1991a, 1991b, 1992 have done extensive work on testing λ 3 = 0 for BVED. But these tests were based on classical inference approach.…”

Section: Tests For Independencementioning

confidence: 99%

“…Here the censoring of lifetimes of two components is due to withdrawals or death of a patient or termination of the study. For the bivariate lifetime distribution, we consider univariate censoring scheme given by Hanagal (1992aHanagal ( , 1992b, because the patients do not enter at the same time and withdrawal or death of a patient will censor lifetimes of both the components. Also, we assume independence between the censoring time and the lifetimes of both components.…”

Section: Likelihood Constructionmentioning

confidence: 99%

Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

Hanagal

Sharma

2014

Communications in Statistics - Theory and Methods

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Many analyses in the epidemiological and the prognostic studies and in the studies of event history data require methods that allow for unobserved covariates or "frailties". We consider the shared frailty model in the framework of parametric proportional hazard model. There are certain assumptions about the distribution of frailty and baseline distribution. The exponential distribution is the commonly used distribution for analyzing lifetime data. In this paper, we consider shared gamma frailty model with bivariate exponential of Marshall and Olkin (1967) distribution as baseline hazard for bivariate survival times. We solve the inferential problem in a Bayesian framework with the help of a comprehensive simulation study and real data example. We fit the model to the real-life bivariate survival data set of diabetic retinopathy data. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the proposed model and then compare the true values of the parameters with the estimated values for different sample sizes.

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Reliability modelling incorporating load share and frailty

Asha

Raja

Равишанкер

2017

Appl Stoch Models Bus & Ind

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The stochastic behaviour of lifetimes of a two component system is often primarily influenced by the system structure and by the covariates shared by the components. Any meaningful attempt to model the lifetimes must take into consideration the factors affecting their stochastic behaviour. In particular, for a load share system, we describe a reliability model incorporating both the load share dependence and the effect of observed and unobserved covariates. The model includes a bivariate Weibull to characterize load share, a positive stable distribution to describe frailty, and also incorporates effects of observed covariates.We investigate various interesting reliability properties of this model using cross ratio functions and conditional survivor functions. We implement maximum likelihood estimation of the model parameters and discuss model adequacy and selection. We illustrate our approach using a simulation study. For a real data situation, we demonstrate the superiority of the proposed model that incorporates both load share and frailty effects over competing models that incorporate just one of these effects. An attractive and computationally simple cross-validation technique is introduced to reconfirm the claim. We conclude with a summary and discussion. KEYWORDSbivariate Weibull distribution, load sharing dependence, maximum likelihood estimation, positive stable frailty, proportional hazards model 206

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Some Inference Results in Modified Freund's Bivariate Exponential Distribution

Cited by 31 publications

References 6 publications

Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

Bayesian Estimation of Bivariate Exponential Distributions Based on Linex and Quadratic Loss Functions: A Survival Approach with Censored Samples

Bayesian Inference in Marshall–Olkin Bivariate Exponential Shared Gamma Frailty Regression Model under Random Censoring

Reliability modelling incorporating load share and frailty

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