[01] Bright Okore Osu, Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria. [02] Samson Ogu–Egege, Department of Mathematics, Abia State University, Uturu, Nigeria. [03] Emmanuel Inyang, Department of Mathematics, Abia State University, Uturu, Nigeria.

The approximation of distribution due to Egege et al [1] is further extended to a wider approximation called total variation distances between Poisson and Pόlya distribution, using Stein’s Chen method and ω -function to give a non-uniform bound. In this work it was found that the results obtain for non-uniform are better than the results obtained for uniform bound in literature. Polya distribution approximate Poisson sufficiently enough provided r is close to n and N is large. If the upper bound is very small then a good approximation is obtained.

The approximation of distribution due to Egege et al [1] is further extended to a wider approximation called total variation distances between Poisson and Pόlya distribution, using Stein’s Chen method and ω -function to give a non-uniform bound. In this work it was found that the results obtain for non-uniform are better than the results obtained for uniform bound in literature. Polya distribution approximate Poisson sufficiently enough provided r is close to n and N

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