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 X n the fraction of black balls after the nth draw. To investigate the asymptotic properties of X n , we first perform some computational studies. We then show that {X n } forms a martingale, which converges almost surely to a random variable X. The distribution of X is then shown to be absolutely continuous.