On exploring the generalized mixture estimators under simple random sampling and application in health and finance sector

There are numerous studies where data on population units’ auxiliary variables and attributes are simultaneously available. Therefore, due to cost-effectiveness and ease of recording, the study variable and several linearly related auxiliary variables are recorded. These auxiliary variables are commonly observed as quantitative and qualitative (attributes) variables and are jointly used to estimate the study variable’s population mean using a mixture estimator. In order to achieve this, a family of generalized mixture estimators was proposed under simple random sampling with the aim of improving performance under symmetrical and asymmetrical distributions. In addition, the estimator’s behavior for various sample sizes was examined with regard to its convergence to the normal distribution. The suggested generalized mixture estimator’s mean square error is deduced up to the first order of approximation. It is discovered that for the normal, uniform, Weibull, and gamma distributions, the suggested estimator estimates the population mean of the study variable with greater accuracy than the competing estimators. It is also revealed that when the proposed estimator converges to normality, the sample size is at least taken as 110, 1000, and 120. Furthermore, the implementation of three real-life datasets related to the finance and health sectors is also presented to support the proposed estimator’s significance.