Generalized Extreme Value versus Halphen System: Exploratory Study

Abstract

The Halphen system and the generalized extreme-value (GEV) distributions are recommended for the estimation of the hydrological extreme events. The GEV system is widely used, whereas the Halphen distributions are less known by hydrologists. The objective of this study is to compare these two systems on the basis of various criteria. A simulation study was undertaken to assess the errors related to the fit of the Halphen distributions to samples generated by the GEV distribution and vice versa. Results show that in the case of power-tail type, the Halphen type Inverse B (HIB) distribution is more adequate and safer than the Fréchet (EV2) or Gumbel (EV1) distributions especially in the case of the small sample size. For subexponential class of distributions, both Halphen Type A (HA) and Type B (HB) perform better than the Gumbel (EV1) distribution. When considering limiting distribution cases, results show a very similar behavior of EV1, gamma, and inverse gamma distribution with a small advantage to the EV1 distribution. These results as well as the theoretical statistical properties of these systems of distributions indicate that the Halphen distributions can, in some cases, perform better than the GEV system and are good candidate to fit extreme value variables.