Predicting observables from a general class of distributions

AL-Hussaini, Essam K.

doi:10.1016/s0378-3758(98)00228-6

Cited by 98 publications

(33 citation statements)

References 33 publications

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“…Notice that Ghafoori et al (2011) considered Bayesian two-sample prediction bounds as well as Bayes predictive estimations for a future progressively Type-II censored sample in a general form of lifetime models, which proposed by AL-Hussaini (1999) including the Weibull and Pareto models, under the symmetric SEL function. Also, it is important to state that in the mentioned paper, the problem of Bayesian two-sample prediction carried out in AL-Hussaini family models under progressively Type-II censored samples.…”

Section: The Ge Distributionmentioning

confidence: 99%

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

Ghafouri¹,

Rad²,

Doostparast³

2016

JSRI

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Abstract. Statistical prediction analysis plays an important role in a wide range of fields. Examples include engineering systems, design of experiments, etc. In this paper, based on progressively Type-II right censored data, Bayesian two-sample point and interval predictors are developed under both informative and non-informative priors. By assuming a generalized exponential model, prediction bounds as well as Bayes point predictors are obtained under the squared error loss (SEL) and the Linear-Exponential (LINEX) loss functions for the order statistic in a future progressively Type-II censored sample with an arbitrary progressive censoring scheme. The derived results may be used for prediction of total time on test in lifetime experiments. In addition to numerical method, Gibbs sampling procedure (as Markov Chain Monte Carlo method) are used to assess approximate prediction bounds and Bayes point predictors under the SEL and LINEX loss functions. The performance of the proposed prediction procedures are also demonstrated via a Monte Carlo simulation study and an illustrative example, for each method.

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Section: The Ge Distributionmentioning

confidence: 99%

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

Ghafouri¹,

Rad²,

Doostparast³

2016

JSRI

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“…For example, the experimenters or the manufacturers would like to have the bounds for the life of their products so that their warranty limits could be plausibly set and customers purchasing manufactured products would like to know the bounds for the life of the product to be purchased. For different application areas, the reader can see [36] [37]. The prediction of progressive Type-II censored data from the Gompertz and Rayleigh distributions has considered, respectively, by [38] [39].…”

Section: Introductionmentioning

confidence: 99%

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Abushal¹,

AL-Zaydi²

2017

OJS

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The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

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“…[13] used conditional argument to develop prediction intervals for future Weibull order statistics. [5] also considered the Bayesian prediction problem for a large class of lifetime distributions. A numerical approach to Bayesian prediction for the twoparameter WE distribution was considered by [10].…”

Section: Introductionmentioning

confidence: 99%

One-sequence and two-sequence prediction for future Weibull records

Bdair¹,

Raqab²

2016

JSTA

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Based on record data, prediction of the future records from the two-parameter Weibull distribution is studied. First we consider the sampling based procedure to compute the Bayes estimates and also to construct symmetric credible intervals. Secondly, we consider one-sequence and two-sequence Bayes prediction of the future records based on some observed records. The Monte Carlo algorithms are used to compute simulation consistent predictors and prediction intervals for future unobserved records. A numerical simulation study is conducted to compare the different methods and a real data set involving the annual rainfall recorded at Los Angeles Civic Center during 132 years is analyzed to illustrate the procedures developed here.

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Predicting observables from a general class of distributions

Cited by 98 publications

References 33 publications

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

Bayesian Two-sample Prediction with Progressively Censored Data for Generalized Exponential Distribution Under Symmetric and Asymmetric Loss Functions

Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

One-sequence and two-sequence prediction for future Weibull records

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