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We propose a way of finding a Stein type characterization of a givenabsolutely continuous distribution $\mu$ on $\R$ which is motivated by aregression property satisfied by an exchangeable pair $(W,W')$ where $\calL(W)$is supposed or known to be close to $\mu$. We also develop the exchangeablepairs approach within this setting. This general procedure is then specializedto the class of Beta distributions and as an application, a convergence ratefor the relative number of drawn red balls among the first $n$ drawings from aPolya urn is computed.

Stein's method of exchangeable pairs for absolutely continuous, univariate distributions with applications to the Polya urn model