Statistical inference for stress-strength reliability using inverse Lomax lifetime distribution with mechanical engineering applications

Tolba, Ahlam H.; Ramadan, Dina A.; Almetwally, Ehab M.; Jawa, Taghreed M.; Sayed-Ahmed, Neveen

doi:10.2298/tsci22s1303t

Cited by 7 publications

(4 citation statements)

References 35 publications

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“…The parameters θ and α, which are assumed to be independent and follow the gamma prior distribution with parameters a and b, are estimated using the Bayesian estimation (BE) approach in this section, see [28].…”

Section: Bayesian Estimation Methodsmentioning

confidence: 99%

Bayesian and Non-Bayesian Inference for The Generalized Power Akshaya Distribution with Application in Medical

Hamdy

Almetwally

2023

Computational Journal of Mathematical and Statistical Sciences

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Generalized power Akshaya distribution is a brand-new two-parameter distribution that builds on the Akshaya distribution first introduced by [1]. The lifetime data is intended to be modelled by this distribution. The generalised power Akshaya's parameters are estimated using both the non-Bayesian and Bayesian approaches in this work. The weighted least square estimation (WLSE), least square estimation (LSE), Cramer-von-Mises estimation (CVME), Anderson and Darling (AD) method of estimation, maximum product Space estimators (MPSE), and maximum likelihood estimation (MLE), six non-Bayesian estimation methods, are used to find the model parameters. The parameters of the suggested distribution were also determined using the squared error loss function and Bayesian estimating (BE) under independent gamma priors. The unknown parameters have been estimated using the Bayesian approach using Markov chain Monte Carlo (MCMC). Additionally, the parameters' average width of the confidence intervals and coverage probability are computed. Additionally, the reliable intervals for Bayesian estimates of the unknown parameters calculated.

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Section: Bayesian Estimation Methodsmentioning

confidence: 99%

Bayesian and Non-Bayesian Inference for The Generalized Power Akshaya Distribution with Application in Medical

Hamdy

Almetwally

2023

Computational Journal of Mathematical and Statistical Sciences

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“…Sabry et al [ 19 ] introduced the inference of fuzzy reliability model for inverse Rayleigh distribution. Tolba et al [ 20 ] discussed fuzzy statistical inference for stress-strength reliability using inverse Lomax lifetime distribution. Mohamed et al [ 21 ] obtained fuzzy inference of reliability analysis for Type II Half logistic Weibull distribution.…”

Section: Fuzzy Historymentioning

confidence: 99%

Data analysis for COVID-19 deaths using a novel statistical model: Simulation and fuzzy application

et al. 2023

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This paper provides a novel model that is more relevant than the well-known conventional distributions, which stand for the two-parameter distribution of the lifetime modified Kies Topp–Leone (MKTL) model. Compared to the current distributions, the most recent one gives an unusually varied collection of probability functions. The density and hazard rate functions exhibit features, demonstrating that the model is flexible to several kinds of data. Multiple statistical characteristics have been obtained. To estimate the parameters of the MKTL model, we employed various estimation techniques, including maximum likelihood estimators (MLEs) and the Bayesian estimation approach. We compared the traditional reliability function model to the fuzzy reliability function model within the reliability analysis framework. A complete Monte Carlo simulation analysis is conducted to determine the precision of these estimators. The suggested model outperforms competing models in real-world applications and may be chosen as an enhanced model for building a statistical model for the COVID-19 data and other data sets with similar features.

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“…According to Kleiber and Kotz, 40 the inverse Lomax distribution has been studied in a range of domains, including stochastic modelling, economics, statistics sciences, reliability analysis, and life-testing. 41 The Inverse Lomax distribution was used by Ziegel 42 to get Lorenz to construct relationships between sorted data. In McKenzie et al, 43 this lifetime distribution was applied to geophysical data, specifically the diameters of ground fibers in California.…”

Section: Introductionmentioning

confidence: 99%

“…In statistical applications, this is one of the most important lifetime models. According to Kleiber and Kotz, 40 the inverse Lomax distribution has been studied in a range of domains, including stochastic modelling, economics, statistics sciences, reliability analysis, and life‐testing 41 …”

Section: Introductionmentioning

confidence: 99%

Statistical inference for multi stress–strength reliability based on progressive first failure with lifetime inverse Lomax distribution and analysis of transformer insulation data

Ramadan

Almetwally

Tolba

2023

Quality & Reliability Eng

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This research aims to develop a multireliability inference method for stress–strength variables based on progressive first failure and an inverse Lomax distribution. This research examines the difficulties associated with estimating the stress–strength reliability function, R, when X, Y, and Z are drawn from three different Inverse Lomax distributions. On the basis of progressive first‐failure censored samples, reliability estimators for multi‐stress–strength Inverse Lomax distributions are estimated using the maximum likelihood, maximum product of spacing, and Bayesian estimation methods. The Bayes estimate of R is obtained using the MCMC method for a symmetric loss function. Monte Carlo simulations and real‐data applications are used to assess and compare the performance of the various suggested estimators.

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Statistical inference for stress-strength reliability using inverse Lomax lifetime distribution with mechanical engineering applications

Cited by 7 publications

References 35 publications

Bayesian and Non-Bayesian Inference for The Generalized Power Akshaya Distribution with Application in Medical

Bayesian and Non-Bayesian Inference for The Generalized Power Akshaya Distribution with Application in Medical

Data analysis for COVID-19 deaths using a novel statistical model: Simulation and fuzzy application

Statistical inference for multi stress–strength reliability based on progressive first failure with lifetime inverse Lomax distribution and analysis of transformer insulation data

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