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In this paper, we introduce a new four-parameter version of the traditional Weibull distribution. It is able to provide seven shapes of hazard rate, including constant, decreasing, increasing, unimodal, bathtub, unimodal then bathtub, and bathtub then unimodal shapes. Some basic characteristics of the proposed model are studied, including moments, entropies, mean deviations and order statistics, and its parameters are estimated using the maximum likelihood approach. Based on the asymptotic properties of the estimators, the approximate confidence intervals are also taken into consideration in addition to the point estimators. We examine the effectiveness of the maximum likelihood estimators of the model's parameters through simulation research. Based on the simulation findings, it can be concluded that the provided estimators are consistent and that asymptotic normality is a good method to get the interval estimates. Three actual data sets for COVID-19, engineering and blood cancer are used to empirically demonstrate the new distribution's usefulness in modeling real-world data. The analysis demonstrates the proposed distribution's ability in modeling many forms of data as opposed to some of its well-known sub-models, such as alpha power Weibull distribution. [ABSTRACT FROM AUTHOR]

The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility. This addition is beneficial in a variety of fields, including reliability, economics, engineering, biomedical science, biological research, environmental studies, and finance. For modeling real data, several expanded classes of distributions have been established. The modified alpha power transformed approach is used to implement the new model. The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models. It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters. Precise expressions for quantiles, moments, incomplete moments, moment generating function, characteristic generating function, and entropy expression are among the determined attributes of the new distribution. The point and interval estimates are studied using the maximum likelihood method. Simulation research is conducted to illustrate the correctness of the theoretical results. Three applications to medical and engineering data are utilized to illustrate the model's flexibility. [ABSTRACT FROM AUTHOR]

In this paper, the maximum likelihood and Bayesian estimation methods are considered to estimate the unknown parameters, reliability, and hazard rate functions of the Nadarajah–Haghighi (NH) distribution based on adaptive type‐I progressive hybrid censoring (ATIPHC) scheme. The Bayesian estimation is obtained under the assumption of independent gamma priors. The Bayes estimators cannot be obtained in closed form, therefore Lindley's approximation and Markov chain Monte Carlo (MCMC) method are used to solve this problem. The approximate confidence (ACIs) and credible intervals are also considered. To compare the efficiency of the different proposed estimators, a simulation study is considered and the performance of the different estimators are compared using mean square error (MSE) and interval length criterion. Finally, one real data set is analyzed in order to show how these mentioned estimators can be applied in practice. The simulation and real data analysis showed that the Bayes estimates have the smallest MSEs and the BCIs have the smallest lengths compared to their conventional counterparts. [ABSTRACT FROM AUTHOR]

In this paper, expected Bayesian (E‐Bayesian) estimation for the simple step–stress model based on type‐II censoring scheme is considered. The case of exponential distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E‐Bayesian estimation is discussed by considering three different prior distributions for the hyperparameters. The E‐Bayesian estimators as well as the corresponding E‐posterior risks are obtained by using squared error and linear‐exponential (LINEX) loss functions. Some properties of the E‐Bayesian estimators are also derived. We conduct a simulation study to compare the various estimators and a simulated and real data sets are analyzed to show the applicability of the different estimators. The numerical results show that the E‐Bayesian estimators perform better than the classical and Bayesian estimators. [ABSTRACT FROM AUTHOR]

This paper introduced the generalized quadratic hazard rate distribution. This new distribution generalizes several well-known distributions such as generalized exponential, generalized Rayleigh, and generalized linear hazard rate. Some statistical and reliability properties of the new distribution were discussed. The maximum likelihood estimates of its unknown parameters were obtained by simulation. The proposed model and other derived results were utilized for fitting real data set and it was shown that the new distribution provided a better fit than some other known distributions. [ABSTRACT FROM AUTHOR]