Comparison of methods for estimating the parameters of the non-stationary GEV model
In frequency analysis, data must generally be independent and identically distributed (i.i.d), which implies that they must meet the statistical criteria of independence, stationarity and homogeneity. In reality, the probability distribution of extreme events can change with time, indicating the existence of non-stationarity. The objective of the present study was to develop efficient estimation methods for the use of the GEV distribution for quantile estimation in the presence of non-stationarity. Parameter estimation in the non-stationary GEV model is generally done with the Maximum Likelihood Estimation method. In this work, we suggest two other estimation methods: the Generalized Maximum Likelihood Estimation (GML) and the generalization of the L-moment method for the non-stationary case. A simulation study was carried out to compare the performances of these three estimation methods in the case of the stationary GEV model (GEV0), the non-stationary case with a linear dependence (GEV1), and the non-stationary case with a quadratic dependence on covariates (GEV2). The non-stationary GEV model was also applied to a case study from the State of California to illustrate its potential.