Hazard rate estimation of a mixture model with censored lifetimes

Ahn, Suneung; Park, C. S.; Kim, H. M.

doi:10.1007/s00477-006-0082-1

Cited by 16 publications

(8 citation statements)

References 9 publications

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“…Estimation of hazard rate functions is considered by [47] for two-parameter decreasing hazard rate distributions, by [23] for the inverse Gaussian distribution, by [34] for the linear hazard rate distribution, and by [1] for a mixture distribution with censored lifetimes. [47] use MLEs, [23] uses MLEs and UMVUEs, [34] use MLEs obtained via the EM algorithm, and [1] use MLEs and a Bayesian approach. Estimation of mean deviation is considered by [22] for the normal distribution and by [48] for the Pearson type distribution.…”

Section: Discussionmentioning

confidence: 99%

On the Estimation for the Weibull Distribution

Alizadeh¹,

Rezaei

Bagheri

2015

Ann. Data. Sci.

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Here, we consider estimation of the pdf and the CDF of the Weibull distribution. The following estimators are considered: uniformly minimum variance unbiased, maximum likelihood (ML), percentile, least squares and weight least squares. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the ML estimator performs better than others.

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Section: Discussionmentioning

confidence: 99%

On the Estimation for the Weibull Distribution

Alizadeh¹,

Rezaei

Bagheri

2015

Ann. Data. Sci.

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“…As mentioned above, when using the Bayesian approach, it is necessary to employ both a likelihood function and a prior distribution to estimate the posterior distribution. A natural-conjugate prior distribution is employed as a likelihood function when they are of the same functional form [22][23][24][25]. Applying Bayesian statistics and using prior knowledge accumulated in previous stages of the design process, also helps to reduce the sample size required to meet a product's reliability specifications [11].…”

Section: Inference Method-bayesian and Non-bayesian Approachesmentioning

confidence: 99%

Bayesian Methods for Reliability Demonstration Test for Finite Population Using Lot and Sequential Sampling

Jeon

Ahn

2018

Sustainability

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The work proposed a reliability demonstration test (RDT) process, which can be employed to determine whether a finite population is accepted or rejected. Bayesian and non-Bayesian approaches were compared in the proposed RDT process, as were lot and sequential sampling. One-shot devices, such as bullets, fire extinguishers, and grenades, were used as test targets, with their functioning state expressible as a binary model. A hypergeometric distribution was adopted as the likelihood function for a finite population consisting of binary items. It was demonstrated that a beta-binomial distribution was the conjugate prior of the hypergeometric likelihood function. According to the Bayesian approach, the posterior beta-binomial distribution is used to decide on the acceptance or rejection of the population in the RDT. The proposed method in this work could be used to select item providers in a supply chain, who guarantee a predetermined reliability target and confidence level. Numerical examples show that a Bayesian approach with sequential sampling has the advantage of only requiring a small sample size to determine the acceptance of a finite population.

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“…In this work, we focus on the method proposed by Ahn et al (2007) to determinate the hyper parameters a, b, c and d of the Gamma prior, this technique is based on bootstrap method. We use same steps that Garthwaite et al (2004) and Ali et al (2013).…”

Section: Elicitation Of Hyper Parametermentioning

confidence: 99%

On Bayesian Premium Estimators for Gamma Lindley Model under Squared Error Loss Function and Linex Loss Function

Sadoun¹,

Zeghdoudi²,

Attoui³

et al. 2017

Journal of Mathematics and Statistics

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Abstract:We consider the Gamma Lindley distribution (GaL) as the conditional distribution of (X|θ,γ), we focus on the estimation of the Bayesian premium under squared error loss function (symmetric) and linearexponential (Linex) loss function (asymmetric), using informative priors (the Gamma prior). Because of its difficulty and non-linearity, we use a numerical approximation for computing the Bayesian premium. Finally, a simulation and comparative study with varying sample sizes are given.

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Hazard rate estimation of a mixture model with censored lifetimes

Cited by 16 publications

References 9 publications

On the Estimation for the Weibull Distribution

On the Estimation for the Weibull Distribution

Bayesian Methods for Reliability Demonstration Test for Finite Population Using Lot and Sequential Sampling

On Bayesian Premium Estimators for Gamma Lindley Model under Squared Error Loss Function and Linex Loss Function

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