Amani Alrumayh

Bounded response variables, such as rates, proportions, and indices, frequently arise in the applied sciences and require regression models that respect the unit interval support, rather than relying on Gaussian regression. In this work, we propose a new regression model for continuous bounded data based on the unit Gumbel–logistic distribution as a flexible alternative to the existing models available in the literature. By reparameterizing the underlying distribution in terms of a location-type parameter directly linked to the covariate structure, our proposal enables the effect of explanatory variables on the response to be modeled in a natural and interpretable way. The proposed regression is derived from the reparameterization of the unit Gumbel–logistic distribution, which possesses a simple probability density function and a closed-form cumulative distribution function, which facilitates the derivation of its main properties. Parameter estimation is carried out using the maximum likelihood estimation method, and the finite-sample performance of the estimators is evaluated through an extensive Monte Carlo simulation study, comprising simulations for residual analysis and for the model. The proposed regression model is further compared with nine established competitors, including the beta, unit Kumaraswamy, unit Lindley, and unit log-log regression models, using two real-data applications. In both datasets, the unit Gumbel–logistic regression model achieved the highest log-likelihood and the lowest AIC, AICc, and BIC, outperforming its closest competitor, the beta regression model. Residual diagnostics and quantile-process analysis confirmed stable, well-behaved parameter estimates in both applications, supporting the unit Gumbel–logistic regression model as a valuable addition to the toolkit of regression models for bounded data.

Modeling real-world data is important in engineering, finance, environmental science, and medical science. Probability distributions are widely used to model such data. However, no single distribution can adequately fit all types of data, which creates a need for flexible distributions. In this study, a new extension of the Chris Jerry distribution (CJD), called the inverse Chris Jerry distribution (ICJD), is introduced using the inverse transformation technique. The probability density function of the ICJD can take right-skewed, reverse J, and inverted bathtub shapes. Its hazard rate function can also take upside-down and decreasing shapes. Several properties of the ICJD are derived, including the mode, harmonic mean, moments, inverse moments, conditional moments, incomplete moments, and order statistics. The model parameter is estimated using 15 estimation methods, and a simulation study is carried out to compare their performance. The simulation results show that the estimators perform consistently as the sample size increases, with the maximum likelihood method performing best. The modeling ability of the ICJD is demonstrated using two real datasets from environmental science and reliability engineering. The results show that the ICJD provides a better fit than the existing inverted distributions considered for both datasets, demonstrating its usefulness in modeling annual flood discharge rates and repair times of an airborne communication transceiver.

A new and enhanced extension of the XLindley distribution termed the sized-biased XLindley distribution (SBXLD), has been introduced. This new model explores two specific variants: the length-biased XLindley distribution and the area-biased XLindley distribution. Various crucial properties such as moments, moment generating function, quantile function, survival, and hazard functions, mean residual life function, and Rényi entropy have been derived and extensively investigated. For parameter estimation, five distinct methods have been employed to estimate the model parameters. Through a comprehensive simulation study, the most effective estimation method has been identified. The applicability and efficiency of the SBXLD model have been demonstrated using two datasets from different domains. It has been observed that the SBXLD model effectively analyzed these datasets and yielded superior results compared to other competitive distributions under consideration.

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.

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.

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.