Abdulaziz S. Alghamdi

Estimation of the population distribution function is an important problem in survey sampling with a variety of applications in social sciences, medical studies, environmental research and economics and in industrial quality control. When auxiliary information is not effectively used, the existing estimators under simple random sampling (SRS) may have low precision. This study considers a novel enhanced estimator for the population distribution function based on the use of two auxiliary variables which are correlated with the study variable, motivated by the desire to improve estimation accuracy and stability. The proposed estimator is based on simple random sampling and the bias and mean square error expressions are derived to first order of approximation. Mean square error and percentage relative efficiency are used to assess the efficiency of the estimator. An empirical validation is performed through a numerical investigation using simulated and real data sets. It is found that the proposed estimator is more efficient and stable, and more accurate than traditional estimators under realistic sampling condition. So, the proposed methodology is reliable and practically useful for contributing to the development of efficient estimation procedures in sampling theory and applications.

Estimation of population proportion is a significant problem in survey sampling and has wide application in social sciences, economics, agriculture, medicine, and public health. The accuracy of estimators can be significantly improved by effectively using auxiliary information. This study proposes an improved generalized class of estimators for estimating the population proportion using two auxiliary attributes. First-order approximation of the mathematical property is obtained for the proposed class, including the expressions for the bias and mean square error (MSE). Theoretical comparisons are made with the traditional sample proportion estimator and some existing estimators that are available in the literature. Analytical conditions under which the proposed generalized class performs better than the other estimators are also determined. In order to analyze the practical performance of the proposed methodology, numerical and simulation studies are carried out on the real and artificially generated population. The results of the experiments confirm that the proposed generalized class consistently yields lower MSE and higher PRE than the traditional estimators. It is concluded that the proposed generalized class is a reliable and efficient alternative to the population proportion estimation for practical survey sampling applications having appropriate auxiliary attributes.

This paper presents an efficient improved generalized class of estimators for the precise estimation of the population distribution function using auxiliary information. Estimation of the population distribution function is a crucial aspect of statistical inference, particularly in survey sampling and applied research, where data of the entire population is often inaccessible. Conventional estimators, although popular, may be inefficient if they do not optimally exploit the information on the auxiliary variables associated with the variable under investigation. To overcome this problem, a new class of estimators is proposed by incorporating the known parameters of the auxiliary variables in a functional form. The bias and mean squared error (MSE) of the suggested and existing estimators are obtained under regularity conditions for large samples. Theoretically, the proposed estimators are shown to have lower MSE than the traditional estimators. The results indicate that using additional information significantly improves estimation accuracy. Thus, the proposed class is an important addition to the literature on survey sampling and estimation of distribution functions. This research contributes useful techniques for researchers and offers guidance to enhance estimation accuracy in empirical studies.

The correct estimation of the population variance plays a vital role in the sampling procedure in surveys, especially when simple random sampling techniques are used. In this work, we propose a new generalized statistical inference in order to estimate the population variance using auxiliary information. We can use the relationship between the study variable and the auxiliary variable to construct a novel generalized class of estimators that is better performing in terms of minimum mean squared error (MSE) and has a higher percentage of relative efficiency than the traditional estimators. The proposed methodology is based on the existing methods of inference with the introduction of modifications to cover the known population parameters of additional auxiliary variables, like the mean, the coefficient of variation, skewness, or kurtosis. Theoretical properties such as bias and mean squared error are obtained with regard to the first-order approximation. The performance of the proposed class of estimators is checked by comparing with that of the classical variance estimators in different population conditions based on real-life data sets and a simulation study. The numerical findings have indicated that the suggested class of estimators is more effective compared to classical methods, especially in cases where there is a very high linear correlation between the auxiliary and the study variables. Also, the estimators are robust, as confirmed using various sample sizes and population structures. The research has made a significant contribution to the development of statistical procedures in survey sampling because the practical and efficient tools provided in the study were useful in estimating the variance. The results have been of great importance when applied by researchers and practitioners active in large-scale surveys. Subsequently, in the case of efficient utilization of auxiliary information, it is feasible to have more accurate and cost-effective statistical inference.

The beta regression model (BRM) is designed to model continuous response variables constrained to the open interval (0, 1). It is particularly suitable for analyzing proportions, rates, and other fractional data. Maximum likelihood estimation (MLE) is the most common way to estimate parameters in the BRM. However, when multicollinearity is present, i.e., when explanatory variables exhibit high intercorrelation, the MLE may produce unstable and biased parameter estimates, inflated variance, and increased scalar mean squared error (MSE), ultimately undermining the model's statistical reliability. To address the effects of multicollinearity, some biased estimators have been proposed for the BRM. In this study, we introduce a new almost unbiased estimator for the BRM. A theoretical comparison of the proposed estimator with existing estimators is derived using the matrix mean squared error (MMSE) and MSE. The performance of the proposed estimator is subsequently assessed and contrasted with existing estimators via a comprehensive Monte Carlo simulation study and applied to two real-world datasets. The simulation and applications consistently show that the proposed estimator is better than other existing estimators, providing more accurate and stable parameter estimates for the BRM under multicollinearity.

This research focuses on estimating the population median within a stratified random sampling framework by using robust statistical measures with transformation-based methodologies. An efficient estimator aims to minimize both the bias and the variance, thereby reducing the overall mean squared error (MSE, leading to more reliable outcomes. We introduce an improved class of proposed estimators that utilizes transformation techniques to effectively address data variability and enhance estimation accuracy. To evaluate their performance, we derive expressions for bias and mean square error (MSE) up to the first-order approximation for both existing and newly developed estimators, establishing theoretical conditions for their effectiveness. Additionally, the proposed estimators are compared with traditional methods using simulated populations generated from different probability distributions and actual datasets. The results indicate that the newly introduced estimators improve precision and efficiency in median estimation, yielding more reliable outcomes. When assessed against conventional estimators, the findings demonstrate that the new estimators outperform in terms of the percent relative efficiency criterion.

This study estimates the population median through stratified random sampling, which enhances accuracy by ensuring the proper representation of key population groups. The proposed class of estimators based on transformations effectively handles data variability and enhances estimation efficiency. We examine bias and mean square error expressions up to the first-order approximation for both existing and newly introduced estimators, establishing theoretical conditions for their applicability. Moreover, to assess the effectiveness of the suggested estimators, five simulated datasets derived from distinct asymmetric distributions (gamma, log-normal, Cauchy, uniform, and exponential), along with actual datasets, are used for numerical analysis. These estimators are designed to significantly enhance the precision and effectiveness of median estimation, resulting in more reliable and consistent outcomes. Comparative analysis using percent relative efficiency (PRE) reveals that the proposed estimators perform better than conventional approaches.

Two-phase sampling is an effective sampling approach that is useful in sample surveys when prior auxiliary information is not available. When two variables have an association, the ranks of the auxiliary variable are proportional to the study variable. Therefore, we can use these rankings to improve the accuracy of the estimators. In this article, we estimate the overall mean of the study variable based on extreme values and the ranks of the auxiliary variable. The properties of the proposed estimators with respect to biases and mean squared errors (MSEs) in two-phase sampling are obtained up to first order approximation. We verify the theoretical results and assess the performance of the proposed estimators using three datasets and a simulation study, which show that the proposed estimators outperform other existing estimators in terms of percent relative efficiency (PRE).