Geodesic
Inequalities for the number of high-probability outcomes of a multinomial scheme
Diskretnaya Matematika, Tome 10 (1998) no. 2, pp. 45-51 
V. G. Mikhailov. Inequalities for the number of high-probability outcomes of a multinomial scheme. Diskretnaya Matematika, Tome 10 (1998) no. 2, pp. 45-51. http://geodesic.mathdoc.fr/item/DM_1998_10_2_a2/
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     author = {V. G. Mikhailov},
     title = {Inequalities for the number of high-probability outcomes of a multinomial scheme},
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     volume = {10},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1998_10_2_a2/}
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In this paper, we give a series of lower bounds for the number $w(x)$ of the outcomes of a discrete random variables whose total probability is no less than $x$. Several examples demonstrate that these inequalities, under some conditions, allow us to estimate the function $w(x)$ to very high accuracy. This research was supported by the Russian Foundation for Basic Research, grants 96–01–00531, 96–15–96092.