Regression analysis is a statistical process that utilizes two or more predictor variables to predict a response variable. When the predictors included in the regression model are strongly correlated with each other, the problem of multicollinearity arises in the model. Due to this problem, the model variance increases significantly, leading to inconsistent ordinary least-squares estimators that may lead to invalid inferences. There are numerous existing strategies used to solve the multicollinearity issue, and one of the most used methods is ridge regression. The aim of this work is to develop novel estimators for the ridge parameter “$\gamma$” and compare them with existing estimators via extensive Monte Carlo simulation and real data sets based on the mean squared error criterion. The study findings indicate that the proposed estimators outperform the existing estimators.

Regularization regression techniques are widely used to overcome a model’s parameter estimation problem in the presence of multicollinearity. Several biased techniques are available in the literature, including ridge, Least Angle Shrinkage Selection Operator (LASSO), and elastic net. In this work, we study the performance of the classical LASSO, adaptive LASSO, and ordinary least squares (OLS) methods in high-multicollinearity scenarios and propose some new estimators for estimating the LASSO parameter “k”. The performance of the proposed estimators is evaluated using extensive Monte Carlo simulations and real-life examples. Based on the mean square error criterion, the results suggest that the proposed estimators outperformed the existing estimators.

In medical research and clinical practice, Bayesian survival modeling is a powerful technique for assessing time-to-event data. It allows for the incorporation of prior knowledge about the model’s parameters and provides a more comprehensive understanding of the underlying hazard rate function. In this paper, we propose a Bayesian survival modeling strategy for proportional hazards regression models that employs the Sine-G family of distributions as baseline hazards. The Sine-G family contains flexible distributions that can capture a wide range of hazard forms, including increasing, decreasing, and bathtub-shaped hazards. In order to capture the underlying hazard rate function, we examine the flexibility and effectiveness of several distributions within the Sine-G family, such as the Gompertz, Lomax, Weibull, and exponentiated exponential distributions. The proposed approach is implemented using the R programming language and the STAN probabilistic programming framework. To evaluate the proposed approach, we use a right-censored survival dataset of gastric cancer patients, which allows for precise determination of the hazard rate function while accounting for censoring. The Watanabe Akaike information criterion and the leave-one-out information criterion are employed to evaluate the performance of various baseline hazards.

In this study, we introduced the log-Lomax distribution, a more versatile probabilistic model for capturing various statistical properties. The study was divided into two sections: Modeling stock price exchange rates with the proposed log-Lomax distribution and incorporating log-Lomax features into machine learning models for prediction. In the modeling section, we introduced the log-Lomax distribution, which employed a logarithmic transformation with an exponent parameter. The model was left- and right-skewed, monotonic, inverted, and bathtub-shaped. Some properties were obtained, and several parameter estimation techniques were evaluated using a simulation study. The model was applied to two Nigerian stock exchange rate datasets: Naira-to-Euro and Naira-to-Riyal, as well as the Worcester heart attack patient dataset. The prediction section used insights from modeling methods and machine learning workflows to improve accuracy and reduce overfitting. The predictions were evaluated in two ways: With raw data and features derived from the log-Lomax model. Employing log-Lomax model features, Random Forest, and XGBoost achieved 99.87% accuracy in the Euro dataset, respectively. Random Forest and XGBoost had accuracy rates of 98.67% and 99.33% on the Riyal dataset, respectively, and 91.25% and 88.75% on the heart attack dataset. Random Forests and XGBoost are the preferred models, as they consistently provide the best prediction performance and stability mix across datasets.

Motivated by the connotation of survival Rényi entropy and its related dynamic version, we introduce them in terms of their lower bounds and mean residual life function. Moreover, we illustrate the relation between survival Rényi entropy and some of measures of information. Furthermore, the hazard rate order implies ordering of dynamic survival Rényi entropy. Our models are considered a more comprehensive version of generalized order statistics and give some properties and characterization results. Finally, a non-parametric estimation of survival Rényi entropy is included based on real COVID-19 data and simulated data.

Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for life distributions. In some reliability processes, such as convolution, mixture, and homogeneous shock models, the closure characteristics of the proposed class-test statistic are investigated. To compare the proposed class-test against some competitive tests, the Weibull, linear failure rate (LFR), and Makeham distributions are evaluated. In addition, the relationship between sample size, level of confidence, and critical values is considered to assess the efficacy of the proposed class-test. Furthermore, a Monte Carlo null distribution critical points simulation and some applications of the censored and uncensored data are performed to demonstrate the validity of the proposed class-test in reliability analysis.