On the max-semistable limit of maxima of stationary sequences with missing values

Abstract

Let { X n } be a stationary sequence with marginal distribution in the domain of attraction of a max-semistable distribution. This includes all distributions in the domain of attraction of any max-stable distribution and also other distributions like some integer-valued distributions with exponential type tails such as the Negative Binomial case. We consider the effect of missing values on the distribution of the maximum term. The pattern of occurrence of the missing values must be either iid or strongly mixing. We obtain the expression of the extremal index for the resulting sequence. The results generalize and extend the ones obtained for the max-stable domain of attraction.