One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data

El-Din, M. M. Mohie; Shafay, A. R.

doi:10.1007/s00362-011-0426-x

Cited by 28 publications

(8 citation statements)

References 31 publications

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“…showing that its derivative is a negative function, then they proved that J(α = 0) > 0 and J(α = ∞) < 0, which mean that J(α) has a unique root in (0, ∞), thereforeβ also is exist and unique. Also, they proved thatα andβ indeed maximizes the function l in (5). The proof in our case is simple when we follow the steps in the proof of Ghitany et al [17].…”

Section: The Existence and Uniqueness Of The Mlessupporting

confidence: 54%

“…In prediction intervals, we depend on the previous data to predict the future observations with a specified probability. Prediction intervals were discussed by many authors, examples of these papers are as follows: Mohie El-Din and Shafay [5], obtained the Bayesian prediction intervals depending on progressively Type-II censored data. Also Bayesian prediction intervals based on the Type-I hybrid censored data were studied by Shafay and Balakrishnan [6].…”

Section: Introductionmentioning

confidence: 99%

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Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

El-Din

Abu‐Moussa

2018

Journal of the Egyptian Mathematical Society

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In this paper, we make a statistical inference for the Gompertz distribution based on multiply Type-I censored data, where we determine a censoring time point for each unit in the life time test. Estimation of the parameters is obtained using maximum likelihood method and Bayesian method, also the asymptotic confidence intervals for the parameters are constructed based on the approximate of the Fisher information matrix. The necessary condition for existence and uniqueness of the maximum likelihood estimators is discussed. The Bayesian estimates are obtained depending on the squared error loss function, linear exponential loss function and the generalized entropy loss function. The One-sample Bayesian prediction intervals are constructed for the unobserved lifetimes in the same sample. A real data example is presented to illustrate the methods of inference developed here. Finally, the simulation study is executed to compare the performance of the proposed methods.

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Section: The Existence and Uniqueness Of The Mlessupporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

El-Din

Abu‐Moussa

2018

Journal of the Egyptian Mathematical Society

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“…Several authors have studied progressive Type-II censoring and properties of order statistics arising from such a progressively censored life-test. Some key references are Aggarwala and Balakrishnan [1], Cramer and Iliopoulos [2], Raqab et al [3], Mohie El-Din and Shafay [4], and Balakrishnan and Cohen [5]. The disadvantages of the progressive Type-II censoring scheme are that the time of the experiment can be very long if the units are highly reliable.…”

Section: Introductionmentioning

confidence: 99%

Statistical Inference for Pareto Distribution based on Progressive Type-I Hybrid Censoring Scheme

El-Din¹,

Shafay²,

Nagy³

et al. 2017

IJCA

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In this paper, the maximum likelihood and Bayesian estimations are developed based on progressive Type-I hybrid censored sample from the Pareto distribution. The Bayesian estimators for the unknown parameters are computed using the squared error loss function. Also, the point and interval Bayesian predictions for the unobserved failures from the same sample and that from the future sample are derived. Moreover, a Monte Carlo simulation study is carried out to compare the performance of the maximum likelihood and the Bayesian estimators. Finally, numerical example is presented for illustrating all the inferential procedures developed here.

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“…As in the case of estimation, a predictor can be either a point or an interval. Bayesian prediction for future observations from the exponential distribution has been discussed by many authors, including [11], [12], [13], [14], [15], [16], [17], [18], and [19].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples

El-Din¹,

Abdel-Aty²,

Shafay³

et al. 2014

AJTAS

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Abstract:In this paper, the maximum likelihood and Bayesian estimations are developed based on the pooled sample of two independent Type-II censored samples from the left truncated exponential distribution. The Bayesian estimation is discussed using different loss functions. The problem of predicting the failure times from a future sample from the sample population is also discussed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the maximum likelihood estimator with the Bayesian estimators. Finally, an illustrative example is presented to demonstrate the different inference methods discussed here.

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One- and two-sample Bayesian prediction intervals based on progressively Type-II censored data

Cited by 28 publications

References 31 publications

Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

Statistical Inference for Pareto Distribution based on Progressive Type-I Hybrid Censoring Scheme

Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples

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