In this article, a new extension of the standard Laplace distribution is introduced for house price modeling. Certain important properties of the new distribution are deducted throughout this study. We used the new extension of the Laplace model to conduct a thorough economic risk assessment utilizing several metrics, including the value-at-risk (VaR), the peaks over a random threshold value-at-risk (PORT-VaR), the tail value-at-risk (TVaR), the mean of order-P (MO^P), and the peaks over a random threshold based on the mean of order-P (PORT-MO^P). These metrics capture different facets of the tail behavior, which is essential for comprehending the extreme median values in the Boston house price data. Notably, PORT-VaR improves the risk evaluations by incorporating randomness into the selection of the thresholds, whereas VaR and TVaR focus on measuring the potential losses at specific confidence levels, with TVaR offering insights into significant tail risks. The MO^P method aids in balancing the reliability goals while optimizing the performance in the face of uncertainty.

This paper introduces a new four-parameter additive model, named xgamma-Burr XII distribution, by considering two competing risks: the former has the xgamma distribution and the latter has the Burr XII distribution. A graphical description of the xgamma-Burr XII distribution is presented, including plots of the probability density function, hazard rate and reversed hazard rate functions. The xgamma-Burr XII density has different shapes such as decreasing, unimodal, approximately symmetric and decreasing-unimodal. The main statistical properties of the proposed model are studied. The unknown model parameters, reliability, hazard rate and reversed hazard rate functions are estimated via the maximum likelihood method. The asymptotic confidence intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are also obtained. A simulation study is carried out to evaluate the performance of the maximum likelihood estimates. In addition, three real data are applied to show the superiority of the xgamma-Burr XII distribution over some known distributions in real-life applications.

This paper suggests an extensive inferential method for the Power Pratibha Distribution (PPD) under Unified Hybrid Censoring Schemes (UHCSs), since there is a growing interest in flexible models in both reliability and service operations. This work studies the PPD model using standard Maximum Likelihood Estimation methods and modern Bayesian approaches too. Using a complex architecture, UHCS simulates tests more closely to what is done in practice than by using more basic censoring schemes. Using analysis, the probability and statistical ranges are carefully calculated for the parameters. Tests demonstrate that Bayesian estimation gives better results than many other methods for estimation, especially when the dataset is not very large and when a lot of data is missing. Real-world tests of electromigration failure data and banking service times help to test the methods. In both situations, the PPD shows it can be used successfully in different reliability settings. By joining advanced censoring models and reliable statistical methods, this research gives a helpful toolset to experts in reliability analysis and statistics.

In recent years, there has been growing interest in discrete probability distributions due to their ability to model the complex behavior of real-world count data. In this paper, a new discrete mixture distribution based on two Weibull components is introduced, constructed using the general discretization approach. Several important statistical properties of the proposed distribution, including the survival function, hazard rate function, alternative hazard rate function, moments, quantile function, and order statistics are derived. It was concluded from the descriptive measures that the discrete mixture of two Weibull distributions transitions from being positively skewed with heavy tails to a more symmetric and light-tailed form. This demonstrates the high flexibility of the discrete mixture of two Weibull distributions in capturing a wide range of shapes as its parameter values vary. Estimation of the parameters is performed via maximum likelihood under Type II censoring scheme. A simulation study assesses the performance of the maximum likelihood estimators. Furthermore, the applicability of the proposed distribution is demonstrated using two real-life datasets. In summary, this paper constructs the discrete mixture of two Weibull distributions, investigates its statistical characteristics, and estimates its parameters, demonstrating its flexibility and practical applicability. These results highlight its potential as a powerful tool for modeling complex discrete data.

In this paper, two different families are mixed: the exponentiated and new Topp–Leone-G families. This yields a new family, which we named the mixture of the exponentiated and new Topp–Leone-G family. Some statistical properties of the proposed family are obtained. Then, the mixture of two exponentiated new Topp–Leone inverse Weibull distribution is introduced as a sub-model from the mixture of exponentiated and new Topp–Leone-G family. Some related properties are studied, such as the quantile function, moments, moment generating function, and order statistics. Furthermore, the maximum likelihood and Bayes approaches are employed to estimate the unknown parameters, reliability and hazard rate functions of the mixture of exponentiated and new Topp–Leone inverse Weibull distribution. Bayes estimators are derived under both the symmetric squared error loss function and the asymmetric linear exponential loss function. The performance of maximum likelihood and Bayes estimators is evaluated through a Monte Carlo simulation. The applicability and flexibility of the MENTL-IW distribution are demonstrated by well-fitting two real-world engineering datasets. The results demonstrate the superior performance of the MENTL-IW distribution compared to other competing models.

The Bayesian approach offers a flexible, interpretable and powerful framework for statistical analysis, making it a valuable tool to help in making optimal decisions under uncertainty. It incorporates prior knowledge or beliefs about the parameters, which can lead to more accurate and informative results. Also, it offers credible intervals as a measure of uncertainty, which are often more interpretable than confidence intervals. Hence, the Bayesian approach is utilized to estimate the parameters, reliability function, hazard rate function and reversed hazard rate function of a new competing risks model. A squared error loss function as a symmetric loss function and a linear exponential loss function as an asymmetric loss function are employed to derive the Bayesian estimators. Credible intervals of the parameters, reliability function, hazard rate function and reversed hazard rate function are obtained. Predicting future observations is important in many fields, from finance and weather forecasting to healthcare and engineering. Thus, two-sample prediction (as a special case of the multi-sample prediction) for future observation is considered. An adaptive Metropolis algorithm is applied to conduct a simulation study to evaluate the performance of the Bayes estimates and predictors. Moreover, two applications of medical and engineering data sets are used to test and validate the theoretical results, ensuring that they are accurate, applicable to real-world scenarios and contribute to the understanding of the world and inform decision-making.