Geodesic
Multinomial and Krawtchouk Approximations to the Generalized Multinomial Distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 117-133

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The generalized multinomial distribution is approximated by multinomial distributions and also by finite signed measures resulting from the corresponding multivariate Krawtchouk expansion. Bounds for the total variation norm and the $\ell_\infty$-norm are presented. The method used is a multivariate extension of that in [B. Roos, Theory Probab. Appl., 45 (2000), pp. 258–272], although additional complications occur.
Keywords: generalized multinomial distribution, multivariate Krawtchouk expansion, signed measures, $\ell_\infty$-norm.
Mots-clés : multinomial approximation, total variation norm 
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     author = {B. Roos},
     title = {Multinomial and {Krawtchouk} {Approximations} to the {Generalized} {Multinomial} {Distribution}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     volume = {46},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a5/}
}
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B. Roos. Multinomial and Krawtchouk Approximations to the Generalized Multinomial Distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 1, pp. 117-133. http://geodesic.mathdoc.fr/item/TVP_2001_46_1_a5/