Hypothesis testing for the population mean and variance based on r-size biased samples

The present research deals with hypothesis testing for the population mean and variance based on r-size biased samples. Specifically, consistent and asymptotically normally distributed estimators of the mean and the variance of a population are proposed and utilized in developing hypothesis tests for the mean and the variance of a distribution. Two different approaches originating, respectively, from plug-in and bootstrap ideas are developed. A Monte Carlo study is carried out to examine the performance of both methods on controlling type I error rate as well as evaluating their power. Finally, the analysis of a real world data set illustrates the benefits incurred from utilizing the proposed methodology.