Estimation methods for the ratio of medians of three-parameter lognormal distributions containing zero values and their application to wind speed data from northern Thailand

Abstract

Wind speed has an important impact on the formation and dispersion of fine particulate matter (PM), which can cause several health problems. During the transition from the winter to the summer season in northern Thailand, the wind speed has been low for longer than usual, which has resulted in fine PM accumulating in the air. Motivated by this, we have identified a need to investigate wind speed due to its effect on PM formation and dispersion and to raise awareness among the general public. The hourly windspeed can be approximated by using confidence intervals for the ratio of the medians of three-parameter lognormal distributions containing zero values. Thus, we constructed them by using fiducial, normal approximation, and Bayesian methods. By way of comparison, the performance measures for all ofthe proposed methods (the coverage percentage, lower and upper error probabilities (LEP and UEP,respectively), and expected length) were assessed via Monte Carlo simulation. The results of Monte Carlo simulation studies show that the Bayesian method provided coverage percentages close to the nominal confidence level and shorter intervals than the other methods. Importantly, it maintained a good balance between LEP and UEP even for large variation and percentage of zero-valued observations. To illustrate the efficacy of our proposed methods, we applied them to hourly wind speed data from northern Thailand.

Keywords

• Wind speed
• Particulate matter
• Confidence intervals
• Ratio of medians
• Fiducial
• Normal approximation