การเปรียบเทียบช่วงความเชื่อมั่นสำหรับมัธยฐานของการแจกแจงแบบเลขชี้กำลัง

Abstract

This aim of this study is to compare interval estimation methods for the population median of exponential distribution considering from coverage probabilities and average widths based on the Bayesian method, The inverting a likelihood ratio test method, The variance stabilizing transformation method and the Bayesian bootstrap method. We conducted the simulation studies based on sample sizes of 10, 15, 20, 30, 40, 50, 100, 150 and 200 and population median of 1, 5, 15, 30, 50 and 100. The Monte Carlo simulation is conducted for 10,000 times with 90%, 95% and 99% confidence level for each situation.

Results of this study showed that the Bayesian method and the Bayesian bootstrap method provided coverage probabilities close to the nominal level in all situations but the average width of the Bayesian bootstrap method was narrower than the Bayesian method in the case of small sample sizes. The inverting a likelihood ratio test method provided the widest average width while the variance stabilizing transformation method provided the narrowest average width in all cases of the study. However, the coverage probabilities of all methods tend to be close to the nominal level when the sample sizes were increased.