Analyzing L-moments, Maximum Likelihood, and Maximum Product of Spacings Estimation Methods for Modeling Climate Extremes

Abstract

Choice of model and estimation method plays a vital role in dealing extremes, especially when the interest is in the extreme upper quantiles. Pearson Type-3 (PE3) probability distribution is frequently used due to its proficiency in effectively accommodating asymmetrical and non-normal data distributions. The location (μ), shape (σ), and scale (γ) parameters of PE3 play a crucial role in determining and controlling skewness, spread, and position of the distribution respectively. The objective of this study is to assess and contrast the impacts of three parameter estimation methods L-moments (LM), Maximum Likelihood Estimation (MLE), and Maximum Product of Spacing (MPS) for the Pearson Type-3 (PE3) distribution. Therefore, empirical analyses are conducted using real world data with diverse degrees of skewness and moderate sample size to compare the estimated parameters of each method against the true parameters. The data being considered is the series of annual maximum rainfall, obtained from 16 different meteorological observatories in zone D and E of Pakistan. This study underscores the importance of selecting an appropriate estimation method tailored to the data's characteristics, highlighting that no single method excels in all scenarios. In conclusion, MPS method is particularly effective for datasets exhibiting severe skewness and kurtosis, allowing it to handle extreme distributions well. In contrast, the LM method performs effectively with datasets that show mild skewness and kurtosis. However, the MLE method struggles when applied to skewed datasets, making it less suitable for such distributions. These insights are crucial for improving the reliability of extreme event modeling and providing a stronger foundation for accurate method selection.