A new urn model

Abstract

In this paper, we propose a new urn model. A single urn contains b black balls and w white balls. For each observation, we randomly draw m balls and note their colors, say k black balls and m − k white balls. We return the drawn balls to the urn with an additional ck black balls and c(m − k) white balls. We repeat this procedure n times and denote by Xn the fraction of black balls after the nth draw. To investigate the asymptotic properties of Xn, we first perform some computational studies. We then show that {Xn} forms a martingale, which converges almost surely to a random variable X. The distribution of X is then shown to be absolutely continuous.