Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

Eraikhuemen, Innocent Boyle; Mohammed, Fadimatu Bawuro; Sule, Ahmed Askira

doi:10.9734/ajpas/2020/v7i230178

Cited by 3 publications

(3 citation statements)

References 25 publications

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“…Aijaz et al [3] studied Bayesian analysis of inverse Topp-Leone distribution under different loss functions. Eraikhuemen et al [9] introduced Bayesian and maximum likelihood estimation of the shape parameter of exponential inverse exponential distribution. Abd AL-Fattah et al [1] introduced Bayesian estimation and prediction for exponentiated generalized inverted Kumaraswamy distribution based on dual generalized order statistics.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation and Prediction for Exponentiated Inverted Topp-Leone Distribution

Albadawy,

Ashour,

EL-Helbawy

et al. 2024

Computational Journal of Mathematical and Statistical Sciences

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This paper focuses on Bayesian estimation for the shape parameters, reliability and hazard rate functions of the exponentiated inverted Topp-Leone distribution. Bayesian estimation is performed under two different loss functions. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function, based on Type II censored sample. Credible intervals for the parameters, reliability and hazard rate functions are derived. The Bayesian two-sample prediction (point and interval) for a future observation from independent future sample from the same distribution, exponentiated inverted Topp-Leone distribution, is obtained based on Type II censored sample. Numerical illustration is proposed, and some interesting comparisons are presented to investigate the theoretical results through some measurements of accuracy. Moreover, the results are applied to real data set to ensure the theoretical results and to prove the applicability of the exponentiated inverted Topp-Leone distribution in real life.

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Section: Introductionmentioning

confidence: 99%

Bayesian Estimation and Prediction for Exponentiated Inverted Topp-Leone Distribution

Albadawy,

Ashour,

EL-Helbawy

et al. 2024

Computational Journal of Mathematical and Statistical Sciences

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“…Moreover, Singh et al [13] study Bayesian estimators of reliability function based on upper record value and upper record ranked set sample using Lindley's approximation. Eraikhuemen et al [14] discuss Bayesian and maximum likelihood estimation of the shape parameter of the exponential inverse exponential distribution. They use a comparative approach.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution

Bakoban¹,

Aldahlan²

2022

Intelligent Automation &Amp; Soft Computing

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In this article, Bayesian techniques are adopted to estimate the shape parameter of the generalized inverted exponential distribution (GIED) in the case of complete samples. Normal approximation, Lindley's approximation, and Tierney and Kadane's approximation are used for deriving Bayesian estimators. Different informative priors are considered, such as Jeffrey's prior, Quasi prior, modified Jeffrey's prior, and the extension of Jeffrey's prior. Non-informative priors are also used, including Gamma prior, Pareto prior, and inverse Levy prior. The Bayesian estimators are derived under the quadratic loss function. Monte Carlo simulations are carried out to make a comparison among estimators based on the mean square error of the estimates. All estimators using normal, Lindley's, and Tierney and Kadane's approximation techniques perform consistently since the MSE decreases as the sample size increases. For large samples, estimators based on non-informative priors using normal approximation are usually better than the ones using Lindley's approximation. Two real data sets in reliability and medicine are applling to the GIED distribution to assess its flexibility. By comparing the estimation results with other generalized models, we prove that estimating this model using Bayesian approximation techniques gives good results for investigating estimation problems. The models compared in this research are generalized inverse Weibull distribution (GIWD), inverse Weibull distribution (IWD), and inverse exponential distribution (IED).

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“…Bayesian technique has received increasing attention by researchers. For example, Eraikhuemenet al (2020a), Ieren et al (2020), Eraikhuemen et al (2020b), Ieren and Oguntunde (2018), Preda et al (2010), Dey (2010), Aliyu andYahaya (2016), Ahmad et. al.…”

Section: Introductionmentioning

confidence: 99%

Estimating the Shape Parameter of the Exponential-Weibull Distribution using Bayesian Technique

Duru¹

2022

SLUJST

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The Exponenial-Weibull Distribution (EWD) has been found to be useful in modeling and prediction of real life events. Its three parameter property makes it more flexible in modeling/accommodating dataset of different characteristics. However, Bayesian technique which is more robust and efficient in most cases, has not been used to estimate the shape parameter of this very important distribution. In view of this, Bayesian technique has been employed to estimate the shape parameter of the distribution. The performance of the technique is assessed and compared with that of maximum likelihood using Monte-carlo simulation. One informative and two non-informative priors as well as three loss functions were used for the study. The results showed that; Bayesian technique produced estimators with lower MSEs regardless of the chosen sample size and parameter value.

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Bayesian and Maximum Likelihood Estimation of the Shape Parameter of Exponential Inverse Exponential Distribution: A Comparative Approach

Cited by 3 publications

References 25 publications

Bayesian Estimation and Prediction for Exponentiated Inverted Topp-Leone Distribution

Bayesian Estimation and Prediction for Exponentiated Inverted Topp-Leone Distribution

Bayesian Approximation Techniques for the Generalized Inverted Exponential Distribution

Estimating the Shape Parameter of the Exponential-Weibull Distribution using Bayesian Technique

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