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In recent years, the modeling of time-to-events has emerged as a highly promising and dynamic research area. This field has witnessed a surge of research studies dedicated to developing novel statistical methodologies aimed at effectively handling time-to-event phenomena. These studies are motivated by the increasing recognition of the importance of time-related factors in various fields such as medicine, epidemiology, finance, and engineering. Researchers have been actively engaged in proposing innovative approaches to address the complexities associated with time-to-event data. The overarching goal is to enhance our understanding of event occurrence and duration, enabling more accurate predictions and informed decision-making. This research encompasses a wide range of topics, including survival analysis, reliability modeling, and event prediction. The motivation behind these research efforts stems from the need to overcome traditional limitations in time-to-event analysis and to explore new avenues for modeling and interpretation. By introducing advanced statistical techniques, researchers seek to capture the intricate dynamics of event processes, considering factors such as censoring, competing risks, and time-varying covariates. The proliferation of research studies in this domain reflects a collective effort to push the boundaries of statistical modeling and analysis, paving the way for more comprehensive and robust methodologies. As researchers continue to delve deeper into the intricacies of time-to-event data, the impact of these advancements extends to diverse applications, ultimately fostering innovation and progress across interdisciplinary fields. This paper adopts and implements a new statistical approach to propose a family of flexible distributions, namely, a new generalized-O family of distributions. For the newly obtained family, certain mathematical properties such as identifiability, quantile function, rth non-central moment, Lorenz curve, incomplete moments, and the expression of the Bonferroni curve are obtained. Furthermore, an extension of the Weibull model is introduced using the newly developed approach, namely, a new generalized Weibull model. The parameters of the new generalized version of the Weibull model are estimated by adopting a well-known estimation approach. Finally, a data set consists of sixty (60) observations representing the times of the survival of some patients infected by the COVID-19 epidemic is analyzed to illustrate the new generalized Weibull model.

The Weibull distribution is considered one of the Type-I Generalized Extreme Value (GEV) distribution, and it plays a crucial role in modeling extreme events in various fields, such as hydrology, finance, and environmental sciences. Bayesian methods play a strong, decisive role in estimating the parameters of the GEV distribution due to their ability to incorporate prior knowledge and handle small sample sizes effectively. In this research, we compare several shrinkage Bayesian estimation methods based on the squared error and the linear exponential loss functions. They were adopted and compared by the Monte Carlo simulation method. The performance of these methods is assessed based on their accuracy and computational efficiency in estimating the scale parameter of the Weibull distribution. To evaluate their performance, we generate simulated datasets with different sample sizes and varying parameter values. A technique for pre-estimation shrinkage is suggested to enhance the precision of estimation. Simulation experiments proved that the Bayesian shrinkage estimator and shrinkage pre-estimation under the squared loss function method are better than the other methods because they give the least mean square error. Overall, our findings highlight the advantages of shrinkage Bayesian estimation methods for the proposed distribution. Researchers and practitioners in fields reliant on extreme value analysis can benefit from these findings when selecting appropriate Bayesian estimation techniques for modeling extreme events accurately and efficiently.

It is essential to use compound families in statistical modeling for asymmetric-positive-skewed reliability and relief in real-life data for a number of reasons, including the capacity to capture underlying patterns and characteristics in the data more accurately. The current work introduces a novel compound and continuous G family of probability distributions characterized by two parameters, denoted as the compounded two-parameters general Rayleigh geometric family of probabilistic distributions. The research involves rigorous calculations to ascertain and analyze the relevant mathematical properties of this newly proposed family. We present aging notions under the new family, providing corresponding density, hazard, and survival functions. Notably, a specific emphasis is placed on the examination of the reciprocal-Weibull baseline model, both from a mathematical and statistical perspective, in a dedicated section of the study. To generate various multivariate and bivariate type distributions, the copula method is employed. These newly derived models hold significant utility for effectively modeling the multivariate and bivariate data. The study showcases the wide applicability in different sides under real-life datasets. The presented applications serve as concrete demonstrations of the family's effectiveness and versatility in addressing real-world scenarios.

The fitting and modeling of skewed, complex, symmetric, and asymmetric datasets is an exciting research topic in many fields of applied sciences: notably, lifetime, medical, and financial sciences. This paper introduces a heavy-tailed Nadarajah Haghighi model by compounding the heavy-tailed family and Nadarajah Haghighi distribution. The model obtained has three parameters that account for the scale and shape of the distribution. The proposed distribution’s fundamental characteristics, such as the probability density, cumulative distribution, hazard rate, and survival functions, are provided, several key statistical properties are established, and several entropy information measures are proposed. Estimation of model parameters is performed via a maximum likelihood estimator procedure. Further, different simulation experiments are conducted to demonstrate the proposed estimator’s performance using measures like the average estimate, the average bias, and the associated mean square error. Finally, we apply our proposed model to analyze three different real datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing models.

The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.