Geodesic
Poisson approximation via the convolution with Kornya--Presman signed measures
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 628-632

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We present an upper bound for the total variation distance between the generalized polynomial distribution and a finite signed measure, which is the convolution of two finite signed measures, one of which is of Kornya–Presman type. In the one-dimensional Poisson case, such a finite signed measure was first considered by K. Borovkov and D. Pfeifer [J. Appl. Probab., 33 (1996), pp. 146–155]. We give asymptotic relations in the one-dimensional case, and, as an example, the independent identically distributed record model is investigated. It turns out that here the approximation is of order $O(n^{-s}(\ln n)^{-{(s+1)/2}})$ for $s$ being a fixed positive integer, whereas in the approximation with simple Kornya–Presman signed measures, we only have the rate $O((\ln n)^{-(s+1)/2})$.
Keywords: asymptotic relation, generalized polynomial distribution, independent and identically distributed record model, Kornya–Presman signed measure, upper bound.
Mots-clés : Poisson approximation, total variation distance 
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     author = {B. Roos},
     title = {Poisson approximation via the convolution with {Kornya--Presman} signed measures},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {628--632},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a14/}
}
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B. Roos. Poisson approximation via the convolution with Kornya--Presman signed measures. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 628-632. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a14/