Estimation and Prediction for Nadarajah-Haghighi  Distribution based on Record Values

Selim, Mahmoud Ali

doi:10.18187/pjsor.v14i2.1854

Cited by 13 publications

(13 citation statements)

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“…The accompanying data set contains actual data on total yearly rainfall (inches) in January from 1880 to 1916. This is data was first analyzed by [9]. There were 37 observations listed below: We begin by determining if the NH distribution is appropriate for evaluating this data set.…”

Section: Real Data Analysismentioning

confidence: 99%

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Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme

et al. 2022

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This work will address the problem of estimating the parameters for the Nadaraj ah–Haghighi (NH) distribution using progressive Type-1 censoring (PT1C) utilizing Bayesian and non-Bayesian approaches. To apply PT1C, censoring times for each stage of censoring needed to be known before the experiment started. To solve this issue of censoring time selection, qauntiles from the NH lifetime distribution will be used as PT1C censoring time points. Maximum likelihood (ML) estimators (MLEs) and asymptotic confidence intervals (ACoIs) are produced with a focus on the censoring technique. Bayes estimates (BEs) and accompanying maximum posterior density (PD) credible interval estimations are also created via the squared error (SEr) loss function. The BEs are evaluated using the Markov Chain Monte Carlo (MCMC) technique and the Metropolis–Hasting (MH) algorithm. An analysis of an actual data set demonstrates the theoretical implications of MLEs and BEs for defined schemes of PT1C samples. Finally, simulation results will be used to compare the performance of the various recommended estimators.

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Section: Real Data Analysismentioning

confidence: 99%

“…In addition, Ref. [9] explored MLEs and BEs using the Lindley approximation for the unknown parameters. Non-Bayesian and Bayesian predictions were also used to make point and interval forecasts for future data.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme

et al. 2022

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“…MirMostafaee et al [37] obtained some recurrence relations for the single and product moments of upper records from the NH model. Selim [38] dealt estimation of NH model parameters through the maximum likelihood and Bayes method based on record values and also considered point and interval predictions of the future record values. Khan and Sharma [39] obtained exact expressions for the Shannon entropy of the NH model based on generalized order statistics.…”

Section: Order Statistics Andmentioning

confidence: 99%

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Ahmadini

Tahir

Alamri

et al. 2021

Mathematical Problems in Engineering

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The extended exponential distribution introduced by Nadarajah and Haghighi in the year 2011, which is nowadays well known as NH distribution, has received increased attention in these days. In this paper, we provide a robust assessment report on the development of three more related extended versions of exponential (or Weibull) distributions. We assessed that which model was published earlier than the other ones and why the pioneer work was not cited properly or overlooked. For example, power generalized Weibull (PGW) introduced by Bagdonavic̆ios and Nikulin (and Nikulin and Haghighi) and extended Weibull by Dimitrakopoulou, Adamidis, and Loukas, which we call here as the DAL model, were published earlier than the NH model. The developments of these three models are stated. A new method for the construction of NH and DAL models is outlined. A literature review on NH and DAL models is presented, and generalized classes from these models are discussed. Furthermore, some corrections in NH moments are suggested, and alternative expressions for moments and incomplete moments of NH and DAL models are also developed.

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“…28 discussed the frequentist and Bayes estimators of the unknown parameters of NHD based on record values. 29 studied the unknown NHD parameters based on upper record values. 30 derived the recurrence relations for the single and product moments for the NHD based on PCS-TII.…”

Section: Introductionmentioning

confidence: 99%

Statistical reliability analysis of electronic devices using generalized progressively hybrid censoring plan

Elshahhat

Azm

2022

Quality & Reliability Eng

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Generalized progressive hybrid censoring plan proposed to overcome the limitation of the progressive hybrid censoring scheme is that it cannot be applied when very few failures may occur before pre-specified terminal time 𝑇. In this paper, the estimating problems of the model parameters, reliability and hazard rate functions of Nadarajah-Haghighi distribution when a sample is available from generalized progressive hybrid censoring have been considered. The maximum likelihood and Bayes estimators have been obtained for any function of the model parameters. Approximate confidence intervals for the unknown parameters and any function of them are constructed. Using independent gamma informative priors, the Bayes estimators of the unknown parameters are derived under the squared-error loss function. Two approximation techniques, namely: Lindley approximation method and Metropolis Hastings algorithm have been used to carry out the Bayes estimates and also to construct the associate highest posterior density credible intervals. The performance of the proposed methods are evaluated through a Monte Carlo simulation study. To select the optimum censoring scheme among different competing censoring plans, different optimality criteria have been considered. A real-life dataset, representing the failure times of electronic devices, is analyzed to demonstrate how the applicability of the proposed methodologies in real phenomenon.

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Estimation and Prediction for Nadarajah-Haghighi Distribution based on Record Values

Cited by 13 publications

References 0 publications

Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme

Bayesian and Non-Bayesian Estimation of the Nadaraj ah–Haghighi Distribution: Using Progressive Type-1 Censoring Scheme

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

Statistical reliability analysis of electronic devices using generalized progressively hybrid censoring plan

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