A Newly-Discovered GPD-GEV Relationship Together with Comparing Their Models of Extreme Precipitation in Summer

It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV (Generalized Extreme Values) distribution can be derived from GPD (Generalized Pareto Distribution). Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT (Peaks Over Threshold)-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values (including the high-end heavy tailed). In comparison, BM (Block Maximum)-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.