A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution

Ali, Sajid; Aslam, Muhammad; Kazmi, Syed Mohsin Ali

doi:10.1016/j.apm.2012.12.008

Cited by 61 publications

(24 citation statements)

References 16 publications

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“…Ali et al (2013), Gupta and Singh (2013) and Al-Mutairi et al (2013). To the best of our knowledge, inference based on LI records is not considered so far in the literature.…”

Section: Introductionmentioning

confidence: 93%

Statistical inference based on Lindley record data

et al. 2016

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Based on record statistics from Lindley distribution, we consider here the problem of estimating the model parameter and predicting the unobserved records. Frequentist and Bayesian analyses are discussed for making some inferences for the model parameter and prediction of unobserved records. Frequentist methods involving maximum likelihood estimation and moments based estimation and Bayesian sampling-based technique are applied for estimating the unknown shape parameter as well as predicting the future unobserved units. The corresponding point predictors and credible intervals of future record values based on an informative set of records can be developed. Real data analysis has been performed for illustrative purposes.

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“…Ali et al (2013), Gupta and Singh (2013) and Al-Mutairi et al (2013). To the best of our knowledge, inference based on LI records is not considered so far in the literature.…”

Section: Introductionmentioning

confidence: 93%

Statistical inference based on Lindley record data

et al. 2016

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“…where t is the estimation value of the parameters. Thus, the EB estimator of σ 2 is the mean of the posterior distribution [29], which can be determined by:…”

Section: Obtain the Eb Estimator Of σ 2 With Respect To The Sel Functionmentioning

confidence: 99%

Empirical Bayes Prediction in a Sequential Sampling Plan Based on Loss Functions

et al. 2019

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The application of empirical Bayes for lot inspection in sequential sampling plans is usually conducted to estimate the proportion of defective items in the lot rather than for hypothesis testing of the variables' process mean. In this paper, we propose the use of empirical Bayes in a sequential sampling plan variables' process mean testing under a squared error loss function and precautionary loss function, for which the prediction is performed to estimate a sequence of the mean when the data are normally distributed in the case of a known mean and unknown variance. The proposed plans are compared with the sequential sampling plan. The proposed techniques yielded smaller average sample number (ASN) and provided higher probability of acceptance (P a ) than the sequential sampling plan.

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“…Recently, Krishna and Kumar (2011) used the Bayesian approach and the maximum probability for an incomplete set of data using various loss functions. On the other hand, Dey et al (1992Dey et al ( , 1999, Ibrahim et al (2012), Ali et al (2013) and Metiri et al (2016) investigated the effect of certain loss functions on Bayes Estimate and the subsequent risk for Lindley's using noninformative and informative priors.…”

Section: Introductionmentioning

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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A study of the effect of the loss function on Bayes Estimate, posterior risk and hazard function for Lindley distribution

Cited by 61 publications

References 16 publications

Statistical inference based on Lindley record data

Statistical inference based on Lindley record data

Empirical Bayes Prediction in a Sequential Sampling Plan Based on Loss Functions

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

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