Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Almongy, Hisham M.; Alshenawy, Fatma Y.; Almetwally, Ehab M.; Abdo, Doaa A.

doi:10.3390/axioms10020100

Cited by 25 publications

(13 citation statements)

References 29 publications

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“…In future work, we intend to discuss ranked set sample for PML distribution as Sabry et al [ 38 ], Sabry and Almetwally [ 39 ], Hassan et al [ 31 ], Noor-ul-Amin et al [ 40 ], and Esemen et al [ 41 ]. Also, we intend to discuss the inference of PML distribution based on censored sample as Hassan and Ismail [ 42 ], Almongy et al [ 43 ] Cho and Lee [ 44 ], and Almetwally et al [ 45 ].…”

Section: Discussionmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime, are provided. The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent. Maximum-likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Bayesian estimation methods of the parameters with independent gamma prior are discussed based on symmetric and asymmetric loss functions. We proposed using the MCMC technique with the Metropolis–Hastings algorithm to approximate the posteriors of the stress-strength parameters for Bayesian calculations. The confidence interval for likelihood and the Bayesian estimation method is obtained for the parameter of the model and stress-strength reliability. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.

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Section: Discussionmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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“…As a result, we employed an informative prior of, and using elective hyper-parameters, the values of hyper-parameters are chosen to satisfy the prior mean, resulting in the expected value of the corresponding parameter; see Refs. [56,57]. The Bayesian estimation based on 12,000 MCMC samples and discarding the first 2000 values as "burn-in" are generated using the M-H sampler technique introduced in Section 3.…”

Section: Simulation Studymentioning

confidence: 99%

Optimal Plan of Multi-Stress–Strength Reliability Bayesian and Non-Bayesian Methods for the Alpha Power Exponential Model Using Progressive First Failure

et al. 2022

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It is extremely frequent for systems to fail in their demanding operating environments in many real-world contexts. When systems reach their lowest, highest, or both extreme operating conditions, they usually fail to perform their intended functions, which is something that researchers pay little attention to. The goal of this paper is to develop inference for multi-reliability using unit alpha power exponential distributions for stress–strength variables based on the progressive first failure. As a result, the problem of estimating the stress–strength function R, where X, Y, and Z come from three separate alpha power exponential distributions, is addressed in this paper. The conventional methods, such as maximum likelihood for point estimation, Bayesian and asymptotic confidence, boot-p, and boot-t methods for interval estimation, are also examined. Various confidence intervals have been obtained. Monte Carlo simulations and real-world application examples are used to evaluate and compare the performance of the various proposed estimators.

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“…For more examples, see [32,33]. From the likelihood function and joint prior function, the joint posterior density function of the IELoP distribution is…”

Section: Bayesian Estimationmentioning

confidence: 99%

Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application

Hassan

Almetwally

Gamoura

et al. 2022

Journal of Mathematics

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In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one-selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.

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Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme

Cited by 25 publications

References 29 publications

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Optimal Plan of Multi-Stress–Strength Reliability Bayesian and Non-Bayesian Methods for the Alpha Power Exponential Model Using Progressive First Failure

Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application

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