MCMC in Analysis of Progressively First Failure Censored Competing Risks Data for Gompertz Model

Bakoban, R. A.; Abd-Elmougod, G. A.

doi:10.1166/jctn.2016.5612

Cited by 20 publications

(9 citation statements)

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“…Furthermore, Ref. [8] introduced the competing risks model into the progressive censoring scheme for the Gompertz distribution and [9] introduced the step-stress partially accelerated life test and derived the MLEs for the acceleration factor in this life test for the progressive first-failure censored Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution

Cai

Gui

2021

Symmetry

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Point and interval estimations are taken into account for a progressive first-failure censored left-truncated normal distribution in this paper. First, we derive the estimators for parameters on account of the maximum likelihood principle. Subsequently, we construct the asymptotic confidence intervals based on these estimates and the log-transformed estimates using the asymptotic normality of maximum likelihood estimators. Meanwhile, bootstrap methods are also proposed for the construction of confidence intervals. As for Bayesian estimation, we implement the Lindley approximation method to determine the Bayesian estimates under not only symmetric loss function but also asymmetric loss functions. The importance sampling procedure is applied at the same time, and the highest posterior density (HPD) credible intervals are established in this procedure. The efficiencies of classical statistical and Bayesian inference methods are evaluated through numerous simulations. We conclude that the Bayes estimates given by Lindley approximation under Linex loss function are highly recommended and HPD interval possesses the narrowest interval length among the proposed intervals. Ultimately, we introduce an authentic dataset describing the tensile strength of 50mm carbon fibers as an illustrative sample.

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Section: Introductionmentioning

confidence: 99%

Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution

Cai

Gui

2021

Symmetry

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“…is aspect is discussed early by Cox [13] using the exponential data. Different properties of the competing risks model are exposed by Crowder [14], Balakrishnan [15], and Bakoban and Abd-Elmougod [16]. Recently, the properties of a competing risks model under the accelerated life test model are discussed by Ganguly and Kundu [17] and Algarni et al [18].…”

Section: Introductionmentioning

confidence: 99%

“…e ALs and CPs of 95% CIs when φ � (1.0, 0.8, 1.5, 1.2). (m 1 , m 2 ) � (33, 23) and (n 11 , n 12 , n 21 , n 22 ) �(17,16,19,4). e random combined sample is selected from both populations, Pop-η 1 and Pop-η 2 , of sizes D � 61 and N � 67, respectively.…”

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confidence: 99%

Inferences for Joint Hybrid Progressive Censored Exponential Lifetimes under Competing Risk Model

Almarashi

Algarni

Daghistani

et al. 2021

Mathematical Problems in Engineering

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The aim of this paper is devoted to the problem of comparative life tests under joint censoring samples from an exponential distribution with competing risks model. This problem is considered under the consideration that only two causes of failure are occurring and the units come from two production lines such that the exponential failure time of units is censored under a hybrid progressive Type-I censoring scheme. Maximum likelihood estimation and different Bayes methods of estimation are discussed. The asymptotic confidence intervals as well as the Bayes credible intervals are established. A real data set representing time to failure on two groups of strain male mice receiving radiation is analyzed for illustrative purposes. All theoretical results are assessed and compared through the Monte Carlo study.

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“…Ref. [ 9 ] investigated a competing risks data model under PFFC from a Gompertz distribution using Bayesian and non-Bayesian methods. Ref.…”

Section: Introductionmentioning

confidence: 99%

Inference for Inverse Power Lomax Distribution with Progressive First-Failure Censoring

Shi

2021

Entropy

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This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

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MCMC in Analysis of Progressively First Failure Censored Competing Risks Data for Gompertz Model

Cited by 20 publications

References 0 publications

Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution

Classical and Bayesian Inference for a Progressive First-Failure Censored Left-Truncated Normal Distribution

Inferences for Joint Hybrid Progressive Censored Exponential Lifetimes under Competing Risk Model

Inference for Inverse Power Lomax Distribution with Progressive First-Failure Censoring

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