Extending the blended generalized extreme value distribution

The generalized extreme value (GEV) distribution is commonly employed to help estimate the likelihood of extreme events in many geophysical and other application areas. The recently proposed blended generalized extreme value (bGEV) distribution modifies the GEV with positive shape parameter to avoid a hard lower bound that complicates fitting and inference. Here, the bGEV is extended to the GEV with negative shape parameter, avoiding a hard upper bound that is unrealistic in many applications. This extended bGEV is shown to improve on the GEV for forecasting heat and sea level extremes based on past data. Software implementing this bGEV and applying it to the example temperature and sea level data is provided.