Geodesic
Approximation by the compound Poisson law
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 583-589 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a specification of the convergence of distributions of sums of independent nonnegative integer random variables to the compound Poisson distribution. The theorems of large deviations and asymptotic expansion under some weak conditions are proved.
Keywords: sums of independent random variables, compound Poisson distribution, large deviations, asymptotic expansions.
Mots-clés : limit distribution, Poisson distribution 
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A. K. Aleshkyavichene; V. Statulevičius. Approximation by the compound Poisson law. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 3, pp. 583-589. http://geodesic.mathdoc.fr/item/TVP_2004_49_3_a7/

[1] Aleškevičiene A., Statulevičius V., “Theorems of large deviations in the approximation by the compound Poisson distribution”, Acta Appl. Math., 78 (2003), 21–34 | DOI | MR | Zbl

[2] Barbour A. D., Chen L. H. Y., Loh W.-L., “Compound Poisson approximation for nonnegative random variables via Stein's method”, Ann. Probab., 20:4 (1992), 1843–1866 | DOI | MR | Zbl

[3] Grigelionis B., “Asymptotic expansions in the compound Poisson limit theorem”, Acta Appl. Math., 58:1–3 (1999), 125–134 | DOI | MR | Zbl

[4] Roos B., “Kerstan's method for compound Poisson approximation”, Ann. Probab., 31:4 (2003), 1754–1771 | DOI | MR | Zbl

[5] Serfozo R. F., “Compound Poisson approximation for sums of random variables”, Ann. Probab., 14:4 (1986), 1391–1398 ; Corrections: ibid. 16:1 (1988), 429–430 | DOI | MR | Zbl | DOI | MR | Zbl

[6] Vellaisamy P., Chaudhuri B., “On compound Poisson approximation for sums of random variables”, Statist. Probab. Lett., 41:2 (1999), 179–189 | DOI | MR | Zbl

[7] Wang Y. H., “From Poisson to compound Poisson approximations”, Math. Sci., 14:1 (1989), 38–49 | MR | Zbl

[8] Wang Y. H., “A compound Poisson convergence theorem”, Ann. Probab., 19:1 (1991), 452–455 | DOI | MR | Zbl

[9] Abramovits M., Stigan I. (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979, 830 pp. | MR