Power-Lindley Generalized Pareto Distribution: A New Approach for Modeling Heavy-Tailed Data

Abstract

This research introduces the Power-Lindley Generalized Pareto Distribution (PL-GPD), a new statistical model designed to better capture heavy-tailed data, which is often found in finance, climate studies, and other fields where extreme events are significant. Unlike existing models like the Normal and Skew Normal Generalized Pareto Distributions (NGPD and SNGPD) by Debbabi et al. (2012) and Debbabi et al. (2016) respectively, which struggle with the complexities of such data, the PL-GPD combines the Power-Lindley distribution (for moderate values) with the Generalized Pareto distribution (for extreme values).Using Maximum Likelihood Estimation (MLE), the PL-GPD was applied to S&P 500 log return data and compared to NGPD and SNGPD based on Akaike Information Criterion (AIC) and Kolmogorov-Smirnov (K-S) statistic. The PL-GPD showed a superior fit, with lower AIC and higher K-S p-values, indicating improved accuracy in modeling rare but impactful events. This enhanced ability to manage extreme data makes PL-GPD especially useful in risk management for fields like finance and insurance.