Statistical analysis of the Gompertz-Makeham model using adaptive progressively hybrid Type-II censoring and its applications in various sciences

Elshahhat, Ahmed; Dutta, Subhankar; Abo-Kasem, Osama E.; Mohammed, Heba S.

doi:10.1016/j.jrras.2023.100644

Cited by 11 publications

(6 citation statements)

References 29 publications

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“…In this application, 34 data points (measured in milligrams/liter) as presented in see Table 1 for vinyl chloride were taken from clean-up-gradient monitoring wells and analyzed. This data set was reported by Bhaumik et al [19] and re-analyzed also by Elshahhat et al [20], Alotaibi et al [21], Elshahhat et al [22]. To verify the flexibility of the MOL model, the MOL distribution is compared with fourteen well-known distributions, (for x > 0 and α, θ , σ ), namely; Marshall-Olkin exponential (MOE(θ , σ )) by Marshall et al [23], Marshall-Olkin Weibull (MOW(α, θ , σ )) by Cordeiro et al [24], Marshall-Olkin Gompertz (MOG(α, θ, σ )) by Eghwerido et al [25], Marshall-Olkin generalized exponential (MOGE(α, θ, σ )) by Ristić et al [26], Marshall-Olkin logistic-exponential (MOLE(α, θ, σ )) by Mansoor et al [27], Marshall-Olkin Nadarajah-Haghighi (MONH(α, θ , σ )) by Lemonte et al [28], Marshall-Olkin alpha power exponential (MOAPE(α, θ, σ )) by Nassar et al [29], alpha power exponential (APE(θ , σ )) by Mahdavi et al [30], generalized-exponential (GE(θ , σ )) by Gupta et al [31], Nadarajah-Haghighi (NH(θ , σ )) by Nadarajah et al [32], Weibull (W(θ , σ )) by Weibull [33], gamma (G(θ , σ )) and exponential (E(σ )) by Johnson et al [34], Lindley (L(σ )) by Lindley [35] distributions.…”

Section: Vinyl Chloridementioning

confidence: 67%

Computational Analysis of Novel Extended Lindley Progressively Censored Data

Alotaibi,

Nassar,

Elshahhat

2024

CMES

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A novel extended Lindley lifetime model that exhibits unimodal or decreasing density shapes as well as increasing, bathtub or unimodal-then-bathtub failure rates, named the Marshall-Olkin-Lindley (MOL) model is studied. In this research, using a progressive Type-II censored, various inferences of the MOL model parameters of life are introduced. Utilizing the maximum likelihood method as a classical approach, the estimators of the model parameters and various reliability measures are investigated. Against both symmetric and asymmetric loss functions, the Bayesian estimates are obtained using the Markov Chain Monte Carlo (MCMC) technique with the assumption of independent gamma priors. From the Fisher information data and the simulated Markovian chains, the approximate asymptotic interval and the highest posterior density interval, respectively, of each unknown parameter are calculated. Via an extensive simulated study, the usefulness of the various suggested strategies is assessed with respect to some evaluation metrics such as mean squared errors, mean relative absolute biases, average confidence lengths, and coverage percentages. Comparing the Bayesian estimations based on the asymmetric loss function to the traditional technique or the symmetric loss function-based Bayesian estimations, the analysis demonstrates that asymmetric loss function-based Bayesian estimations are preferred. Finally, two data sets, representing vinyl chloride and repairable mechanical equipment items, have been investigated to support the approaches proposed and show the superiority of the proposed model compared to the other fourteen lifetime models.

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Section: Vinyl Chloridementioning

confidence: 67%

Computational Analysis of Novel Extended Lindley Progressively Censored Data

Alotaibi,

Nassar,

Elshahhat

2024

CMES

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“…Ri. This configuration makes sure that the experiment ends when we reach the desired number of failures m and that the overall test duration will not deviate too much from the ideal length of time T. This approach was utilized by several writers to estimate many lifetime models, including Nassar and Abo-Kasem, 7 Nassar et al, 8 Sobhi and Soliman, 9 Chen and Gui, 10 Alotaibi et al, 11 Dutta et al, 12 and Elshahhat et al 13 Let y 1:m:n < . .…”

Section: Article Pubsaiporg/aip/advmentioning

confidence: 99%

Analysis of the new complementary unit Weibull model from adaptive progressively type-II hybrid

Alotaibi,

Nassar,

Elshahhat

2024

AIP Advances

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In this study, we look at some estimation issues for complementary unit Weibull distributions in the context of adaptive progressive type-II hybrid censoring. The point and interval estimations of the model parameters, as well as a number of its reliability indices, are explored. The likelihood frequentist approach is used as a classical strategy to obtain the point and approximate confidence ranges. The median parameter of the distribution is produced in a closed form as a function of the shape parameter, while the shape parameter can be obtained iteratively. The squared error loss function and gamma and beta prior distributions are used for evaluating Bayes estimates. The Markov chain Monte Carlo method is used to solve the difficult posterior distribution expression in order to provide Bayes estimates and the highest posterior density credible ranges. A simulation study is done to evaluate the efficacy of various estimating methodologies making use of different circumstances for sample sizes and progressive censoring strategies. Finally, three real-world datasets from veterinary, industrial, and physical applications are examined to highlight the practical importance of the provided methodologies.

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“…They offer several advantages over conventional CSs, including increased flexibility and efficiency. For more details on PCS, one may refer to [2][3][4][5]. However, PCSs can be more complex to design and analyze, and they may not be suitable for all research questions.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and non-bayesian inference for logistic-exponential distribution using improved adaptive type-II progressively censored data

Dutta,

Alqifari,

Almohaimeed

2024

PLoS ONE

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Improved adaptive type-II progressive censoring schemes (IAT-II PCS) are increasingly being used to estimate parameters and reliability characteristics of lifetime distributions, leading to more accurate and reliable estimates. The logistic exponential distribution (LED), a flexible distribution with five hazard rate forms, is employed in several fields, including lifetime, financial, and environmental data. This research aims to enhance the accuracy and reliability estimation capabilities for the logistic exponential distribution under IAT-II PCS. By developing novel statistical inference methods, we can better understand the behavior of failure times, allow for more accurate decision-making, and improve the overall reliability of the model. In this research, we consider both classical and Bayesian techniques. The classical technique involves constructing maximum likelihood estimators of the model parameters and their asymptotic covariance matrix, followed by estimating the distribution’s reliability using survival and hazard functions. The delta approach is used to create estimated confidence intervals for the model parameters. In the Bayesian technique, prior information about the LED parameters is used to estimate the posterior distribution of the parameters, which is derived using Bayes’ theorem. The model’s reliability is determined by computing the posterior predictive distribution of the survival or hazard functions. Extensive simulation studies and real-data applications assess the effectiveness of the proposed methods and evaluate their performance against existing methods.

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Statistical analysis of the Gompertz-Makeham model using adaptive progressively hybrid Type-II censoring and its applications in various sciences

Cited by 11 publications

References 29 publications

Computational Analysis of Novel Extended Lindley Progressively Censored Data

Computational Analysis of Novel Extended Lindley Progressively Censored Data

Analysis of the new complementary unit Weibull model from adaptive progressively type-II hybrid

Bayesian and non-bayesian inference for logistic-exponential distribution using improved adaptive type-II progressively censored data

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