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Background: COVID‐19 has posed substantial challenges to healthcare systems globally, emphasizing the need for robust epidemiological tracking, particularly in regions like Saudi Arabia where distinct variations in case rates necessitate specialized public health strategies. Aims and Objectives: This study aims to identify the most effective model for predicting COVID‐19 trends by analyzing daily time‐to‐event case data across six Saudi regions. The goal is to enhance resource allocation and intervention strategies by gaining a deeper understanding of the epidemic's dynamics and developing a reliable method for early detection of trend changes to prompt timely public health actions. Research Gap: Previous studies have predominantly utilized simpler statistical models such as log‐normal, Gamma, and Weibull distributions, which often fall short in accurately describing the complex behaviors of COVID‐19 case distributions, particularly during peak times and periods of periodicity. This study addresses these shortcomings by employing advanced trigonometrically enhanced models. Methodology: To model daily time‐to‐event COVID‐19 case data from various regions in Saudi Arabia spanning 2020 to 2023, we employed the new trigonometric Weibull distribution from the new trigonometric‐generated P‐class of distributions. Our methodological approach included a comprehensive model validation process, utilizing a comparative analysis across seven distinct estimation techniques. Maximum likelihood estimation proved to be the most effective overall. We also adapted specific classical estimation techniques to fit the unique epidemiological characteristics of each region: Cramer von Mises estimation for Abu 'Urwah, Al‐Aridah, and Al Bada'I; Anderson–Darling estimation for Abha; maximum product spacing estimation for Ad Dammam; and maximum likelihood estimation for Abu 'Arish. This tailored approach allowed for a detailed analysis of regional data, enhancing the accuracy and relevance of our modeling outcomes. Conclusions: The new trigonometric Weibull distribution effectively modeled daily COVID‐19 cases across various regions in Saudi Arabia, demonstrating superior fit and capturing complex epidemic dynamics. This study highlights the new trigonometric Weibull distribution distribution's capability to detect significant trends and periodic fluctuations, enhancing public health response strategies. Its successful application underscores the value of advanced trigonometric models in epidemiological research and pandemic management. [ABSTRACT FROM AUTHOR]

We introduce a new flexible count distribution by combining Bernoulli and Poisson moment exponential (PMEx) distributions. The new model named the Bernoulli PMEx distribution. Some mathematical properties are studied, including the hazard rate function, moments, moment generating function, probability generating function, and dispersion index. A count regression model is also proposed based on this distribution. The maximum likelihood estimation method is used to estimate the model parameters. In the end, three datasets from different fields are utilized for application purposes. The findings show that the new model efficiently analyzed these datasets as compared to Poisson, discrete Pareto, discrete Rayleigh, discrete Burr‐Hatke, and discrete inverted Topp–Leone distributions. [ABSTRACT FROM AUTHOR]

This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]