Count data often exhibit dispersion patterns that the standard Poisson regression model struggles to handle, particularly in cases of overdispersion or underdispersion. The generalized Poisson regression model (GPRM) provides a more flexible alternative, extending the Poisson model to better accommodate such variations. However, parameter estimation in the GPRM typically relies on the generalized Poisson maximum likelihood estimator, which can be problematic when multicollinearity exists among explanatory variables. Biased estimation methods can be used to address this issue. This study explores the Liu estimator as a potential solution for reducing multicollinearity in the GPRM. We also propose different strategies for selecting the Liu parameter to improve estimation accuracy. The theoretical properties of the generalized Poisson Liu estimator are examined, and its performance is compared to that of the generalized Poisson maximum likelihood estimator using matrix mean squared error and scalar mean squared error as evaluation criteria. To assess its effectiveness, we conduct Monte Carlo simulations and apply the method to a carbon dioxide emission dataset in Canada. The results show that the generalized Poisson Liu estimator, particularly with an optimally chosen Liu parameter, outperforms the standard generalized Poisson maximum likelihood estimator in reducing estimation error in the presence of multicollinearity.

A flexible distribution for the analysis of bounded data is proposed. The new model is generalized through the transmuted approach, and the resultant model is named “transmuted modified Lehmann-type II distribution.” A comprehensive analysis of key characteristics is performed, including the shape of the model, survival, and hazard function, analytical expressions of mode, quantile function, ordinary moments, quantile function, and stress–strength reliability. Some famous entropy measures are also derived. The model parameters have been estimated using four distinct methods, including maximum likelihood estimation, Anderson Darling, Cramer–von Misses, and ordinary least squares. A detailed simulation study is used to evaluate the behavior of all derived estimators. Finally, a dataset was used to demonstrate the utility of the proposed distribution.

The primary focus of all sample surveys is on providing point estimates for the parameters of primary interest, and also estimating the variance associated with those point estimates to quantify the uncertainty. Larger samples and important measurement tools can help to reduce the point estimates’ uncertainty. Numerous effective stratification criteria may be used in survey to reduce variance within stratum. In fine stratification design, the population is divided into numerous small strata, each containing a relatively small number of sampling units as one or two. This is done to ensure that certain characteristics or subgroups of the population are well-represented in the sample. But with many strata, the sample size within each stratum can become small, potentially resulting in higher errors and less stable estimates. The variance estimation process becomes difficult when we only have one unit per stratum. In that case, the collapsed stratum technique is the classical methods for estimating variance. This method, however, is biased and results in an overestimation of the variance. This paper proposes a bootstrap-based variance estimator for the total population under fine stratification, which overcomes the drawbacks of the previously explored estimation approach. Also, the estimator’s properties were investigated. A simulation study and practical application on survey of mental health organizations data were done to investigate properties of the proposed estimators. The results show that the proposed estimator performs well.

In the context of stratified sampling, we develop a nonparametric regression technique to estimating finite population quantiles in model‐based frameworks using a multiplicative bias correction strategy. Furthermore, the proposed estimator’s asymptotic behavior is presented, and when certain conditions are met, the estimator is observed to be asymptotically unbiased and asymptotically consistent. Simulation studies were conducted to determine the proposed estimator’s performance for the three quartiles of two fictitious populations under varied distributional assumptions. Based on relative biases, mean‐squared errors, and relative root‐mean‐squared errors, the proposed estimator can be extremely satisfactory, according to these findings.

Smooth non-parametric quantile function estimators on basis of symmetric kernels exhibit boundary bias due to spill-over near the edges. An improved non-parametric estimator of a quantile function under simple random sampling without replacement is proposed, based on a multiplicative bias corrected distribution function. There is no spill-over around the edges with our new quantile estimator. The proposed quantile estimator's asymptotic properties are investigated. The suggested method is compared to existing estimators using real data set findings, demonstrating the improved performance.