PROBGENEXTVAL: Stata module to Estimate Binary Generalized Extreme Value (GEV) Models

probgenextval performs estimations of binary generalized extreme value (GEV) models. The generalized extreme value (GEV) distribution is a lineage of continuous probability laws that are utilized to characterize extreme values phenomena. It incorporates the Gumbel, Frechet and Weibull distributions lineages also known as type I, II and III extreme value distributions. The generalized extreme value (GEV) distribution, by incorporating the previous three distributions, permits to obtain a continuous spectrum of possible shapes encompassing all the three preceding distributions. In this sense, it is more flexible because it lets the data speak and choose which distribution is more suitable. The command probgenextval estimates a generalized extreme value (GEV) model for a binary dependent variable, typically with one of the outcomes rare, or extremely rare, relative to the other. The command probgenextval can calculate robust and cluster-robust standard errors and remodel results for complex survey designs. The generalized extreme value (GEV) distribution is employed in Extreme Value Theory or Extreme Value Analysis to model the probability of events that are more extreme than any formerly noticed. That is, it is utilized to estimate the risk of extreme, rare events, for example: the 1755 Lisbon Earthquake, the 2004 Indian Ocean Earthquake and Tsunami, Credit Defaults, and the Modeling of COVID-19/CORONAVIRUS. The theory behind the command probgenextval can be found in Calabrese and Osmetti (Journal of Applied Statistics, 2013), and Wang and Dey (The Annals of Applied Statistics, 2010).