Ahmed Hamdi Mansi

This study applies both Bayesian and non-Bayesian methods to estimate the lifetime parameters of the quadratic hazard rate distribution using incomplete lifetime data under progressive Type-II censoring with binomial removal. The three-parameter quadratic hazard rate model generalizes traditional distributions, including linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, parameters, as well as reliability and hazard rate functions, are estimated using maximum likelihood estimation (MLE) and maximum product of spacing (MPS). Asymptotic confidence intervals are derived, with a focus on the delta method. Bayesian inference is then performed under both MLE and MPS approaches using independent informative priors (normal and gamma) and both symmetric (squared error) and asymmetric (linear exponential) loss functions to obtain point estimates and highest posterior density credible intervals. Given the complexity of closed-form Bayesian estimates, Markov chain Monte Carlo methods are employed to sample from the posterior distribution. The precision and consistency of point and interval estimates are assessed using four performance metrics: root mean squared error, mean relative absolute bias, average confidence interval length, and coverage probability. A simulation study explores these criteria across varying sample sizes and censoring schemes. The proposed methods are further validated on real-world data concerning the remaining service time of aircraft windshields. In addition, we analyzed the existence and uniqueness of the estimates before confirming them graphically. Finally, the results indicate that Bayesian approaches outperform non-Bayesian methods in terms of accuracy and robustness, offering valuable insights into reliability testing and decision-making in engineering applications.

Thermodynamics, statistical mechanics, and quantum mechanics are the branches of physics that use entropy and extropy measures. It also seems to quantify the degree of signal uncertainty in information theory. Recently, extropy has been widely used in the literature as a measure of dispersion or uncertainty. Within generalized Farlie-Gumbel-Morgenstern families, the Cambanis bivariate family holds a prominent position as an efficient and adaptable extended family. Motivated by this, our work gives numerous characterizations of Cambanis copula based on order statistics (OSs). Also, we study the negative cumulative residual extropy and various measures of information associated with it for concomitants generalized OSs. Moreover, we study OSs and sequential OSs for each information measure in a computational study. This study offers a few beautiful symmetrical and asymmetric relationships that these information measures satisfy. Additionally, the empirical technique is applied to the Cambanis family to estimate every measure of negative extropy discussed in this work. As a final step, we have examined a bivariate real-world data set for illustrative purposes.

Based on Type-I generalized progressive hybrid censored samples (GPHCSs), the parameter estimate for the unit-half logistic-geometry (UHLG) distribution is investigated in this work. Using maximum likelihood estimation (MLE) and Bayesian estimation, the parameters, reliability, and hazard functions of the UHLG distribution under GPHCSs have been assessed. Likewise, the computation is carried out for the asymptotic confidence intervals (ACIs). Furthermore, two bootstrap CIs, bootstrap-p and bootstrap-t, are mentioned. For symmetric loss functions, like squared error loss (SEL), and asymmetric loss functions, such as linear exponential loss (LL) and general entropy loss (GEL), there are specific Bayesian approximations. The Metropolis–Hastings samplers methodology were used to construct the credible intervals (CRIs). In conclusion, a genuine data set measuring the mortality statistics of a group of male mice with reticulum cell sarcoma is regarded as an application of the methods given.

In statistical modeling, lifetime datasets play an important and significant role. Weighted distributions can be useful to attain the essential purposes relating to the developed distributions’ flexibility and to improve further compliances in data forming; they provide the extension of distributions. The current study suggests a new best-fit probability distribution model based on Pareto distribution. The new model is called Survival Weighted Pareto (SWP) distribution model. Furthermore, the statistical expressions for different properties, which include moments, inverse moments, quantile function, and order statistics, are reported. Moreover, to check the performance and the behavior of different estimators using different sample sizes, a simulation study, which is based on SWP distribution, is performed. According to the simulation results, it is established that the proposed model is a most useful fitted probability model. In addition, an application of the SWP model for three datasets is provided to check the goodness of fit measures of the model.

The paper introduces the hybrid odd exponential-Φ (HOE-Φ) family, a novel framework for generating a continuous distribution characterized by an additional parameter. The extensive statistical properties of this family are derived and explored in detail. Parameter estimation is performed using the maximum likelihood estimation technique. The efficacy and versatility of the proposed model are demonstrated through a comparative analysis involving two distinct real-world datasets.

In this research, we establish the novel sin-G class, an innovative and comprehensive class of trigonometric distributions centered on the sine function. A sin-G class analytical approach comprises calculations for the probability density function and reliability indicators. Various estimation methods were presented to estimate the specified model parameters. Applying randomly created datasets and the provided estimating techniques, the behavior of these variables was investigated. Then, the focus is directed toward a specific member of this class, the novel sin-Lomax distribution, which is established with the Lomax distribution serving as the baseline. Exploring the innovative sin-Lomax distribution’s inferential characteristics, the constructed distribution is then fitted to real datasets, demonstrating the actual application of the Sin-G class.

A flexible distribution for the analysis of bounded data is proposed. The new model is generalized through the transmuted approach, and the resultant model is named “transmuted modified Lehmann-type II distribution.” A comprehensive analysis of key characteristics is performed, including the shape of the model, survival, and hazard function, analytical expressions of mode, quantile function, ordinary moments, quantile function, and stress–strength reliability. Some famous entropy measures are also derived. The model parameters have been estimated using four distinct methods, including maximum likelihood estimation, Anderson Darling, Cramer–von Misses, and ordinary least squares. A detailed simulation study is used to evaluate the behavior of all derived estimators. Finally, a dataset was used to demonstrate the utility of the proposed distribution.

In this article, the odd Lomax Gompertz distribution has been introduced, which is derived by modifying the Gompertz distribution to serve as a baseline model in the odd generalized Lomax distribution. The newly proposed model offers enhanced flexibility and provides a promising alternative for modeling lifetime data. This study seeks to establish a solid theoretical foundation for its application through the exploration of several properties, such as non-central moments, stochastic orderings quantile function, and entropy measure, for the new model. Additionally, by conducting simulation analysis, the performance of the various estimation methods is being assessed, which enables the identification of the most reliable approach for estimating the unknown parameters of the newly developed model. The simulation analysis of the two-risk metrics, namely, value at risk and expected shortfall, revealed the ability of the distribution to capture diverse failure rate patterns, which makes it particularly relevant for assessing financial risks. Finally, the suggested model is practiced to two real-life datasets to provide the compelling evidence of superior flexibility and practical versatility compared to existing models in the literature.

Using the power transformation method, we introduce a generalized version of the unit Gumbel type-2 distribution. The new lifetime distribution is called the power unit Gumbel type-2 distribution (PUGT2D). The new distribution’s statistical and reliability properties are given, and some estimation methods are proposed for estimating the model parameters. The usefulness and flexibility of the new distribution are illustrated with real datasets. Results based on log-likelihood, information statistics, and goodness-of-fit test results showed that the PUGT2D better fits the data than the other competing distributions. Moreover, a new regression model based on the new distribution is introduced and demonstrated to exhibit superior applicability through a numerical example.