An engineering approach to Bayes estimation for the Weibull distribution

Calabria, R.; Pulcini, Gianpaolo

doi:10.1016/0026-2714(94)90004-3

Cited by 120 publications

(79 citation statements)

References 24 publications

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“…We have computed posterior mean m * using (31) and m * * using (32) for the data given in Table 1 considering different sets of values of (μ). Following Calabria and Pulcini [10], we also assume the prior information to be correct if the true value of σ −2 is closed to prior mean μ and is assumed to be wrong if σ −2 is far from μ. We observed that the posterior mode m * appears to be robust with respect to the correct choice of the prior density of σ −2 and also with a wrong choice of the prior density of σ −2 .…”

Section: Sensitivity Of Bayes Estimatesmentioning

confidence: 99%

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Bayes Estimation of Two‐Phase Linear Regression Model

Pandya

Bhatt

Andharia

2011

Journal of Quality and Reliability Engineering

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Let the regression model be Y i = β 1 X i + ε i , where ε i are i. i. d. N (0, σ 2 ) random errors with variance σ 2 > 0 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after X m by change in slope, regression parameter β 2 . The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β 1 , β 2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.

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Section: Sensitivity Of Bayes Estimatesmentioning

confidence: 99%

“…Another loss function, called general entropy (GE) loss function, proposed by Calabria and Pulcini [10], is given by…”

Section: Asymmetric Loss Functionmentioning

confidence: 99%

Bayes Estimation of Two‐Phase Linear Regression Model

Pandya

Bhatt

Andharia

2011

Journal of Quality and Reliability Engineering

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“…provided that the expectation ( − ) exists and is finite [18]. In Figures 1(a) and 1(b), values of ( ) are plotted for the selected values of for = 1 and = −1.…”

Section: Advances In Statisticsmentioning

confidence: 99%

“…Bayesian estimator̂of using uniform prior (17) and posterior density (18), under the assumption of the LINEX loss function (ref. (12)) is obtained aŝ…”

Section: Bayesian Estimators Using Uniformmentioning

confidence: 99%

Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

Kaur

Arora

Mahajan

2015

Advances in Statistics

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Bayesian estimators of Gini index and a Poverty measure are obtained in case of Pareto distribution under censored and complete setup. The said estimators are obtained using two noninformative priors, namely, uniform prior and Jeffreys’ prior, and one conjugate prior under the assumption of Linear Exponential (LINEX) loss function. Using simulation techniques, the relative efficiency of proposed estimators using different priors and loss functions is obtained. The performances of the proposed estimators have been compared on the basis of their simulated risks obtained under LINEX loss function.

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“…Here we consider the asymmetric loss function, namely, GELF, proposed by Calabria and Pulcini [10], is…”

Section: Bayes Estimators Under General Entropy Loss Function (Gelf)mentioning

confidence: 99%

Bayes Estimation of a Two‐Parameter Geometric Distribution under Multiply Type II Censoring

Shah¹,

Patel

2011

Journal of Quality and Reliability Engineering

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We derive Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.

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An engineering approach to Bayes estimation for the Weibull distribution

Cited by 120 publications

References 24 publications

Bayes Estimation of Two‐Phase Linear Regression Model

Bayes Estimation of Two‐Phase Linear Regression Model

Bayesian Estimation of Inequality and Poverty Indices in Case of Pareto Distribution Using Different Priors under LINEX Loss Function

Bayes Estimation of a Two‐Parameter Geometric Distribution under Multiply Type II Censoring

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