Reliability Analysis of the New Exponential Inverted Topp-Leone Distribution with Applications.

The inverted Topp-Leone distribution is a new, appealing model for reliability analysis. In this paper, a new distribution, named new exponential inverted Topp-Leone (NEITL) is presented, which adds an extra shape parameter to the inverted Topp-Leone distribution. The graphical representations of its density, survival, and hazard rate functions are provided. The following properties are explored: quantile function, mixture representation, entropies, moments, and stress-strength reliability. We plotted the skewness and kurtosis measures of the proposed model based on the quantiles. Three different estimation procedures are suggested to estimate the distribution parameters, reliability, and hazard rate functions, along with their confidence intervals. Additionally, stress-strength reliability estimators for the NEITL model were obtained. To illustrate the findings of the paper, two real datasets on engineering and medical fields have been analyzed.

Robust-stein estimator for overcoming outliers and multicollinearity.

Linear regression models with correlated regressors can negatively impact the performance of ordinary least squares estimators. The Stein and ridge estimators have been proposed as alternative techniques to improve estimation accuracy. However, both methods are non-robust to outliers. In previous studies, the M-estimator has been used in combination with the ridge estimator to address both correlated regressors and outliers. In this paper, we introduce the robust Stein estimator to address both issues simultaneously. Our simulation and application results demonstrate that the proposed technique performs favorably compared to existing methods.

Predictors of mental health problems during the COVID-19 outbreak in Egypt in 2021.

Background: With the widespread outbreak of the coronavirus (COVID-19) pandemic, many countries, including Egypt, have tried to restrict the virus by applying social distancing and precautionary measures. Understanding the impact of COVID-19-induced risks and social distancing measures on individuals' mental health will help mitigate the negative effects of crises by developing appropriate mental health services. This study aimed to investigate the most contributing factors that affected individuals' mental health and how individuals' mental health has changed over the lockdown period in Egypt in 2021. Methods: The study draws on a nationally representative sample from the combined COVID-19 MENA Monitor Household Survey conducted by the Economic Research Forum. The data were collected in Egypt by phone over two waves in February 2021 and June 2021. The total number of respondents is 4,007 individuals. The target population is mobile phone owners aged 18-64 years. The 5-item World Health Organization Well-Being Index (WHO-5) is used to assess the individuals' mental health over the past 2 weeks during the pandemic. Penalized models (ridge and LASSO regressions) are used to identify the key drivers of mental health status during the COVID-19 pandemic. Results: The mean value of mental health (MH) scores is 10.06 (95% CI: 9.90-10.23). The average MH score for men was significantly higher than for women by 0.87. Rural residents also had significantly higher MH scores than their urban counterparts (10.25 vs. 9.85). Middle-aged adults, the unemployed, and respondents in low-income households experienced the lowest MH scores (9.83, 9.29, and 9.23, respectively). Individuals' mental health has deteriorated due to the negative impacts of the COVID-19 pandemic. Regression analysis demonstrated that experiencing food insecurity and a decrease in household income were independent influencing factors for individuals' mental health (p < 0.001). Furthermore, anxiety about economic status and worrying about contracting the virus had greater negative impacts on mental health scores (p < 0.001). In addition, women, middle-aged adults, urban residents, and those belonging to low-income households were at increased risk of poor mental health (p < 0.05). Conclusion: The findings reveal the importance of providing mental health services to support these vulnerable groups during crises and activating social protection policies to protect their food security, incomes, and livelihoods. A gendered policy response to the pandemic is also required to address the mental pressures incurred by women.

A new class of efficient and debiased two-step shrinkage estimators: method and application.

This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators' mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators' performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners.

A new estimator for the multicollinear Poisson regression model: simulation and application.

The maximum likelihood estimator (MLE) suffers from the instability problem in the presence of multicollinearity for a Poisson regression model (PRM). In this study, we propose a new estimator with some biasing parameters to estimate the regression coefficients for the PRM when there is multicollinearity problem. Some simulation experiments are conducted to compare the estimators' performance by using the mean squared error (MSE) criterion. For illustration purposes, aircraft damage data has been analyzed. The simulation results and the real-life application evidenced that the proposed estimator performs better than the rest of the estimators.

A New Ridge-Type Estimator for the Gamma Regression Model.

The known linear regression model (LRM) is used mostly for modelling the QSAR relationship between the response variable (biological activity) and one or more physiochemical or structural properties which serve as the explanatory variables mainly when the distribution of the response variable is normal. The gamma regression model is employed often for a skewed dependent variable. The parameters in both models are estimated using the maximum likelihood estimator (MLE). However, the MLE becomes unstable in the presence of multicollinearity for both models. In this study, we propose a new estimator and suggest some biasing parameters to estimate the regression parameter for the gamma regression model when there is multicollinearity. A simulation study and a real-life application were performed for evaluating the estimators' performance via the mean squared error criterion. The results from simulation and the real-life application revealed that the proposed gamma estimator produced lower MSE values than other considered estimators.

A New Ridge-Type Estimator for the Linear Regression Model: Simulations and Applications.

The ridge regression-type (Hoerl and Kennard, 1970) and Liu-type (Liu, 1993) estimators are consistently attractive shrinkage methods to reduce the effects of multicollinearity for both linear and nonlinear regression models. This paper proposes a new estimator to solve the multicollinearity problem for the linear regression model. Theory and simulation results show that, under some conditions, it performs better than both Liu and ridge regression estimators in the smaller MSE sense. Two real-life (chemical and economic) data are analyzed to illustrate the findings of the paper.