Resumen de On statistical model extensions based on randomly stopped extremes

Jordi Valero Baya, Josep Ginebra

• The maxima and the minima of a randomly stopped sample of a random variable, X, together with two newly defned random variables that make X into the maxima or min- ima of a randomly stopped sample of them, can be used to defne statistical model transformation mechanisms. These transformations can be used to defne models for extreme-value data that are not grounded on large sample theory. The relationship between the stopping model and characteristics of the corresponding model transfor- mations obtained is investigated. In particular, one looks into which stopping models make these model transformations into model extensions, and which stopping models lead to statistically stable extensions in the sense that using the model extension a sec- ond time leaves the extended model unchanged. The stopping models under which the extensions based on randomly stopped maxima and their inverses coincide with the ex- tensions based on randomly stopped minima and their inverses are also characterized.

  The advantages of using models obtained through these model extension mechanisms instead of resorting to extreme-value models grounded on asymptotic arguments is il- lustrated by way of examples