On estimation of the population mean in a two-parameter Rayleigh distributed variable with applications to environmental studies

Patarawan Sangnawakij

ABSTRACT: This paper considers parameter estimation for the population mean of a two-parameter Rayleigh distribution. We derive a new variance of the mean estimator and provide a confidence interval using the Waldtype method, the large-sample approach, the method of variance estimate recovery, and bootstrap methods. The performance of these interval estimators is conducted through Monte Carlo simulation. According to the studies, the moment estimator has the smallest mean squared error and bias in estimation. The bootstrap-t confidence interval performs very well in all cases in the study. In particular, this method outperforms the compared confidence intervals for small sample sizes as it covers the mean parameter with a given coverage probability. When sample sizes are large, the confidence intervals using maximum likelihood and moment estimators are superior. Three real-world examples of environmental data are used to demonstrate the approaches in applications.

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^a	Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Pathum Thani 12120 Thailand

* Corresponding author, E-mail: patarawan.s@gmail.com

Received 23 Aug 2024, Accepted 16 Dec 2024