Extreme value analysis with new generalized extreme value distributions: a case study for risk analysis on PM2.5 and PM10 in Pathum Thani, Thailand

Abstract

The paper emphasizes the development and application of the power Garima-generalized extreme value distribution for analyzing extreme values of PM2.5 and PM10 in Pathum Thani, Thailand. A new distribution is derived from the power Garima-generated family, and the generalized extreme value distribution provides a continuous framework for modeling extreme events. Additionally, a discrete version of the proposed distribution, namely the discrete power Garima-generalized extreme value distribution, is provided to handle discrete analog data. The maximum likelihood method is used to estimate the parameters when fitting the model to empirical data. The discrete power Garima-generalized extreme value model was utilized in a study to forecast the highest levels of PM2.5 and PM10 (measured in micrograms per cubic meter) for different return periods, including 2, 5, 10, 15, 20, 25, 30, 50, and 100 years. Both PM2.5 and PM10 show increasing return levels as the return period increases. This work's importance lies in its contribution to understanding and predicting extreme PM2.5 and PM10 values, which is critical for meteorologists and policymakers. By providing tools grounded in extreme value theory, the paper supports informed decision-making, planning, and mitigation strategies against the health impacts associated with these particulate matters.