Geodesic
On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 625-636 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G_i=(1-p_i)E+p_iB_i$ where $0\le p_i\le 1$, $E$ is the distribution concentrated at zero, $B_i$ is an arbitrary one-dimensional distribution, $\displaystyle p=\max_{1\le i\le n}p_i$. Define $$ G=\prod_{i=1}^nG_i,\qquad D=\prod_{i=1}^n\exp(G_i-E). $$ Then $$ \sup_x|G\{(-\infty,x)\}-D\{(-\infty,x)\}|\le cp. $$ 
@article{TVP_1983_28_4_a0,
     author = {A. Yu. Zaitsev},
     title = {On the accuracy of approximation of distributions of sums of independent random variables~{\textendash} which are nonzero with a~small probability~{\textendash} by means of accompanying laws},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {625--636},
     year = {1983},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a0/}
}
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A. Yu. Zaitsev. On the accuracy of approximation of distributions of sums of independent random variables – which are nonzero with a small probability – by means of accompanying laws. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 625-636. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a0/