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The joint progressive Type‐II censoring scheme is an advantageous cost‐saving strategy. In this paper, investigated classical and Bayesian methodologies for estimating the combined parameters of two distinct Lomax distributions employing the joint progressive Type‐II censoring scheme. Maximum likelihood estimators have been derived, and asymptotic confidence intervals are presented. Bayesian estimates and their corresponding credible intervals are calculated, incorporating both symmetry and asymmetry loss functions through the utilization of the Markov Chain Monte Carlo (MCMC) method. The simulation aspect has employed the MCMC approximation method. Furthermore, discussed the practical application of these methods, providing illustration through the analysis of a real dataset. [ABSTRACT FROM AUTHOR]

The proposed article introduces a novel three-parameter lifetime model called an exponentiated extended extreme-value (EEEV) distribution model. The EEEV distribution is characterized by increasing or bathtub-shaped hazard rates, which can be advantageous in the context of reliability. Various statistical properties of the distribution have been derived. The article discusses four estimation methods, namely, maximum likelihood, least squares, weighted least squares, and Cramer-von Mises, for EEEV distribution parameter estimation. A simulation study was carried out ´ to examine the performance of the new model estimators based on the four estimation methods by using the average bias, mean squared errors, relative absolute biases, and root mean square error. The flexibility and significance of the EEEV distribution are demonstrated by analyzing three real-world datasets from the fields of medicine and engineering. The EEEV distribution exhibits high adaptability and outperforms several well-known statistical models in terms of performance. [ABSTRACT FROM AUTHOR]

In this study, we investigated the Inverted Exponentiated Rayleigh Distribution (IERD), a significant and efficient continuous lifetime distribution commonly applied in lifespan research. Our focus was on estimating unknown parameters for a two-parameter inverted exponentiated Rayleigh distribution using unified hybrid censored data. We considered both maximum likelihood and Bayesian estimation approaches. Specifically, we employed the Gibbs within Metropolis–Hastings samplers method to develop approximate Bayes estimators utilizing informative and non-informative priors, along with symmetric and asymmetric loss functions. In addition, we utilized Markov chain Monte Carlo (MCMC) samples to derive maximum posterior density credible intervals. Simulation experiments were conducted to assess the efficacy of the proposed methodologies, and actual data analysis was performed to validate the proposed estimators. [ABSTRACT FROM AUTHOR]

In this study, we explore the practical applications of maximum likelihood and Bayesian estimation methods in the context of progressive type-II censoring, focusing specifically on the Marshall–Olkin extended Gumbel type-II distribution. We begin by computing maximum likelihood estimates for the distribution's parameters and constructing asymptotic confidence intervals. Additionally, we employ the Markov chain Monte Carlo method to establish credible intervals for Bayes estimates, considering both squared error and linear exponential loss functions. To showcase the effectiveness of our approach, we analyze two real datasets and conduct a simulation study to evaluate the performance of our proposed estimators across varying sample sizes. Our findings reveal that the Bayes estimators for the parameters outperform the maximum likelihood estimators. [ABSTRACT FROM AUTHOR]

Using a unified hybrid censoring scheme, this study explores statistical inferences for products with lifetimes following the generalized inverted exponential distribution. The model's parameters are estimated using the maximum likelihood approach. In addition, likelihood functions and asymptotic theories are employed to generate approximate confidence intervals. Moreover, Bayesian estimates based on classical likelihood functions are investigated, considering both asymmetric and symmetric loss functions with prior information. It is recommended to approximate the Bayes estimates using Gibbs sampling, which utilizes the Markov chain Monte Carlo technique to establish credible intervals for the parameters. A numerical example is provided to demonstrate the effectiveness of the proposed methods. Furthermore, a simulation study is conducted to illustrate the confidence intervals and the statistical characteristics of the parameters. [ABSTRACT FROM AUTHOR]

In order to evaluate the competitive advantages and dependability of two products in a competitive environment, comparative lifespan testing becomes essential. We examine the inference problems that occur when two product lines follow the Nadarajah-Haghighighi distribution in the setting of joint type-II censoring. In the present study, we derived the maximum likelihood estimates for the Nadarajah-Haghighi population parameters. Additionally, a Fisher information matrix was constructed based on these maximum likelihood estimations. Furthermore, Bayesian estimators and their corresponding posterior risks were calculated, considering both gamma and non-informative priors under symmetric and asymmetric loss functions. To assess the performance of the overall parameter estimators, we conducted a Monte Carlo simulation using numerical methods. Lastly, a real data analysis was carried out to validate the accuracy of the models and methods discussed. [ABSTRACT FROM AUTHOR]

This study focuses on an innovative life distribution category known as the 'New Better than Renewal used in Moment Generating Function' (NBRUmgf) class. It explores the relationships between this particular aging model and established aging categories, and its applicability within a shock model. Moreover, it investigates the consistency of this aging concept through specific reliability operations, which are pivotal tools in reliability engineering. The research involves computing Pitman's asymptotic efficiencies for this testing method and compares them with alternative approaches. Additionally, the study presents an extensive table of percentiles for the test statistic associated with this proposed technique. To underscore the significance of the study's findings, various real-world datasets are employed, demonstrating the efficacy of our test methodology across diverse types of actual data. [ABSTRACT FROM AUTHOR]