Infinitely Divisible Distributions in Statistical Inference: Heavy-Tailed Distributions and Convolution Models.

摘要

The family of infinitely divisible distributions is shown to provide alternative formulations in several inferential situations. In particular, the family provides heavy-tailed distributions and distributions for use in models involving convolutions, such as signal-plus-noise models. Characterizations of sub-families of the infinitely divisible family are used to obtain statistical tests of membership in those sub-families. Special attention is given to the normal and normal-plus-Poisson sub-families. (Author)