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

Abstract

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.

Keywords:

• Biased sampling
• consistent estimators
• weighted distributions
• asymptotic tests
• bootstrap

2020 Mathematics Subject Classifications:

• 62F03
• 62F12

Acknowledgments

The authors would like to thank the two anonymous referees and the Associate Editor for many helpful comments and suggestions, which have greatly helped in improving the quality and the presentation of this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).