Poisson regression is a popular tool for modeling count data and is applied in medical sciences, engineering and others. Real data, however, are often over or underdispersed, and we cannot apply the Poisson regression. To overcome this issue, we consider a regression model based on the Conway–Maxwell Poisson (COMP) distribution. Generally, the maximum likelihood estimator is used for the estimation of unknown parameters of the COMP regression model. However, in the existence of multicollinearity, the estimates become unstable due to its high variance and standard error. To solve the issue, a new COMP Liu estimator is proposed for the COMP regression model with over‐, equi‐, and underdispersion. To assess the performance, we conduct a Monte Carlo simulation where mean squared error is considered as an evaluation criterion. Findings of simulation study show that the performance of our new estimator is considerably better as compared to others. Finally, an application is consider to assess the superiority of the proposed COMP Liu estimator. The simulation and application findings clearly demonstrated that the proposed estimator is superior to the maximum likelihood estimator.

A new three‐parameter extension of the generalized‐exponential distribution, which has various hazard rates that can be increasing, decreasing, bathtub, or inverted tub, known as the Marshall‐Olkin generalized‐exponential (MOGE) distribution has been considered. So, this article addresses the problem of estimating the unknown parameters and survival characteristics of the three‐parameter MOGE lifetime distribution when the sample is obtained from progressive type‐II censoring via maximum likelihood and Bayesian approaches. Making use of the s‐normality of classical estimators, two types of approximate confidence intervals are constructed via the observed Fisher information matrix. Using gamma conjugate priors, the Bayes estimators against the squared‐error and linear‐exponential loss functions are derived. As expected, the Bayes estimates are not explicitly expressed, thus the Markov chain Monte Carlo techniques are implemented to approximate the Bayes point estimates and to construct the associated highest posterior density credible intervals. The performance of proposed estimators is evaluated via some numerical comparisons and some specific recommendations are also made. We further discuss the issue of determining the optimum progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, two real‐life datasets are analyzed to demonstrate how the proposed methods can be used in real‐life scenarios.

In farming and related fields, numerous connections exist that should be distinguished quantitatively. Several factors affect the various crop yields in different dimensions. These factors may have relation with farmers practices or with quality of soil. In this study, our main focus is to explore the effect of soil and other factors on the wheat yield. Regression modeling plays an important role in the identification of such factors that greatly affect the crops yield. For reliable and valid results, one has to check the data for outliers and other critical results. In this study, we have fitted the regression models with and without satisfying some regression assumptions to determine the factors affecting yield of wheat. For analysis purposes, the required data were collected from the district Multan. It was observed that when the regression assumptions were satisfied, then coefficient of determination (R²) was improved from 45 to 48, R² (adjusted) was improved from 40 to 46, and the standard error of the estimates was reduced from 2.772 to 2.649. These results indicate that the soil characteristics, such as saturation, electrical conductivity, organic matter, phosphorus, potassium, calcium carbonate, and micronutrients (zinc, copper, iron, manganese, and boron), are the significant factors for wheat yield. While among all other factors, urea, chemical coating of seed, use of compost, and previously sown crops are the significant factors for wheat yield.