The max-semistable laws: characterization, estimation and testing

In this talk we present the class of max-semistable distribution functions that appear as the limit, in distribution, of the maximum, suitably centered and normalized, of k_n independent and identically distributed random variables, where {k_n} is an integer-valued geometric sequence with ratio r (larger or equal to 1). This class of distributions includes all the max-stable distributions but also multimodal distributions and discrete distributions. We will characterize the max-semistable laws, discuss the estimation of the parameters and the fractal component and propose a test that allow us to distinguish between max-stable and max-semistable laws.

Join work with Luísa Canto e Castro and Maria da Graça Temido.