E-Bayesian estimations for the cumulative hazard rate and mean residual life based on exponential distribution and record data
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Estimation of lifetime parameters such as reliability and hazard rate is necessary in many systems. Each method of estimation suffers from its own problems such as complexity of computations, high risk and etc. Toward this end, this study employed a new method, E-Bayesian, for estimating the parameters based on exponential distribution and record data. Furthermore, the asymptotic behaviours of E-Bayesian estimations and relations among them have been investigated. Finally, a comparison among the E-Bayesian estimations and older methods are made, using a real data and the Monte Carlo simulation. The computations show that the new method is more efficient than previous methods and is also easy to operate.Keywords:
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We introduce here a new distribution called the power-modified Kies-exponential (PMKE) distribution and derive some of its mathematical properties. Its hazard function can be bathtub-shaped, increasing, or decreasing. Its parameters are estimated by seven classical methods. Further, Bayesian estimation, under square error, general entropy, and Linex loss functions are adopted to estimate the parameters. Simulation results are provided to investigate the behavior of these estimators. The estimation methods are sorted, based on partial and overall ranks, to determine the best estimation approach for the model parameters. The proposed distribution can be used to model a real-life turbocharger dataset, as compared with 24 extensions of the exponential distribution.
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The purpose of this paper is to study the Bayesian Estimation for exponential distribution with a parameter in a exponential failure model.The confidential interval of this distribution is obtained;meanwhile,the Bayesian problems of risks for exponential distributions with one and two parameters are discussed as well.
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Abstract The aim of this paper is to study the Bayesian reliability analysis of the exponential distribution under a precautionary loss function based on zero failure data. In the Bayesian algorithm, the prior distribution of the parameter is assumed to be Gamma distribution. Bayesian and E-Bayesian estimators of the failure rate and reliability of exponential model are obtained under the precautionary loss function. Finally, a practical example is utilized to validate the effectiveness and robustness of the proposed estimators.
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This Chapter, "Overview of Approximate Bayesian Computation", is to appear as the first chapter in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and concepts behind ABC methods with many examples and illustrations.
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In reliability engineering, it is of great significance to predict residual lives of systems. At present, exponential-Weibull distribution is more and more widely used since it can fit complex failure rates. Meanwhile, failure information is available in practical engineering systems, which can be utilized to get more precious estimations. Assuming that the lifetimes of components follows exponential-Weibull distributions, the closed-forms of residual life for typical systems, including series system, parallel system and r-out-of-n: G system are derived with known failure information and the calculation method is presented accordingly. Finally, examples are given to show the proformance of the proposed method. The results show that if the failure information of components is ignored, the residual life estimation results of the system will have a large deviation.
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This is a discussion of the journal article: Construcing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation. The article and discussion have appeared in the Journal of the Royal Statistical Society: Series B (Statistical Methodology).
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This methodological paper in Bayesian econometrics applied to macroeconomic models, presents first the Bayesian estimation of DSGE models, then illustrates the e¤ects of the estimation for a panel of countries, assuming some homogeneity across coun- tries. Under some specifications, the results exhibit more preci- sion about parameters in a panel approach. The gain of precision is important using a panel of small samples of data.
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