On Structural and Asymptotic Properties of Some Classes of Distributions

• Autores: Vladimir Vinogradov
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 97, Nº. 1-3, 2007, págs. 335-351
• Idioma: inglés
• DOI: 10.1007/s10440-007-9117-y
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• Resumen

  • We consider the two-parametric classes of distributions which comprise exponential dispersion models possessing a simple structure. Some of our models are related to Galton-Watson processes and branching diffusions. We study asymptotic properties of related classes of distributions emphasizing their convergence to Poisson-exponential law. We establish/refute infinite divisibility for certain classes of distributions. The critical value for the deflation of zeros from a geometric law which preserves infinite divisibility is determined. A class of distributions related to zero-modified geometric and logarithmic laws is considered.