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\u27 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\u27 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

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

On Developing Ridge Regression Parameters: A Graphical investigation

In this paper we have reviewed some existing and proposed some new estimators for estimating the ridge parameter "k" . All in all 19 different estimators have been studied. The investigation has been carried out using Monte Carlo simulations. A large number of different models were investigated where the variance of the random error, the number of variables included in the model, the correlations among the explanatory variables, the sample size and the unknown coefficients vectors "beta" have been varied. For each model we have performed 2000 replications and presented the results both in term of figures and tables. Based on the simulation study, we found that increasing the number of correlated variable, the variance of the random error and increasing the correlation between the independent variables have negative effect on the MSE. When the sample size increases the MSE decreases even when the correlation between the independent variables and the variance of the random error are large. In all situations, the proposed estimators have smaller MSE than the ordinary least squared and some other existing estimators.Linear Model; LSE; MSE; Monte Carlo simulations; Multicollinearity; Ridge Regression;