Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MT_2021_24_2_a7, author = {S. V. Nagaev}, title = {On the accuracy of approximation of the binomial distribution by the {Poisson} law}, journal = {Matemati\v{c}eskie trudy}, pages = {122--149}, publisher = {mathdoc}, volume = {24}, number = {2}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MT_2021_24_2_a7/} }
S. V. Nagaev. On the accuracy of approximation of the binomial distribution by the Poisson law. Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 122-149. http://geodesic.mathdoc.fr/item/MT_2021_24_2_a7/
[1] Kolmogorov A. N., “Dve ravnomernye predelnye teoremy dlya summ nezavisimykh slagaemykh”, TVP, 1:4 (1956), 426–436
[2] Prokhorov Yu. V., “Asimptoticheskoe povedenie binomialnogo raspredeleniya”, UMN, 8 (1953), 135–142 | Zbl
[3] Tsaregradskii I. P., “O ravnomernom priblizhenii binomialnogo raspredeleniya neogranichenno delimymi zakonami”, TVP, 3:4 (1958), 470–474
[4] Barbour A. D., Hall P., “On the rate of Poisson convergence”, Math. Proc. Cambridge Philos. Soc., 95 (1984), 473–480 | DOI | Zbl
[5] Le Cam L., “An approximation theorem for the Poisson binomial distribution”, Pacific J. Math., 10 (1960), 1181–1197 | DOI | Zbl
[6] Daley D. J., Vere-Jones D., An Introduction to the Theory of Point Processes, v. II, Probability and Its Applications, General Theory and Structure, 2nd revised and extended ed., Springer-Verlag, New York, NY, 2008 | DOI | Zbl
[7] Franken P., “Approximation des Verteilungen von Summen unabhängiger nichtnegativer ganzzahler Zufallsgrössen durch Poissonsche Verteilungen”, Math. Nachr., 23 (1964), 237–340
[8] Hipp C., “Approximation of aggregate claims distribution by compound Poisson distributions”, Insurance Math. Econom., 4 (1985), 227–232 | DOI | Zbl
[9] Kennedy J. E., Quine M. P., “The total variation distance between the binomial and Poisson distributions”, Ann. Probab., 17 (1989), 396–400 | DOI | Zbl
[10] Kruopis Y., “Precision of approximation of the generalized binomial distribution by convolutions of Poisson measures”, Lith. Math. J., 26 (1986), 37–59 | DOI
[11] Makabe H., “On the approximations to some limiting distributions with some applications”, Kōdai Math. Semin. Rep., 14 (1962), 123–133 | Zbl
[12] Novak S. Y., “Poisson approximation”, Probab. Surv., 16 (2019), 228–276 | DOI | Zbl
[13] Serfling R. J., “Some elementary results on Poisson approximation in a sequence of Bernoulli trials”, SIAM Rev., 20 (1978), 567–579 | DOI | Zbl
[14] Zacharovas V., Hwang H-K., “A Charlier–Parseval approach to Poisson approximation and its applications”, Lith. Math. J., 50:1 (2010), 88–119 | DOI | Zbl