Urns & Tubes

Urn models play an important role to express various basic ideas in probability theory. Here we extend this urn model with tubes. An contains coloured balls, which can be drawn probabilities proportional the numbers of balls each colour. For colour a tube is assumed. These tubes have different sizes (lengths). The idea that after drawing ball from it dropped corresponding We consider two associated distributions. first-full distribution on colours gives for full first, before any other negative natural captures number k all are first time draws.This paper uses multisets systematically describe these and distributions urns setting, fully multivariate form, three standard modes (multinomial, hypergeometric, Pólya).