A q-Pólya urn model and the q-Pólya and inverse q-Pólya distributions

► A q-Pólya urn model is introduced, extending the classical Pólya urn model. ► A q-Pólya distribution and an inverse q-Pólya distribution are defined and their properties are studied. ► As particular cases the q-hypergeometric and inverse q-hypergeometric distributions are examined. ► The q-hypergeometric distribution is used to estimate the unknown number of errors in a manuscript.