Article
On Distribution Functions of Certain Block Sequences
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Abstract
In this paper we study the sequence x1 < x2 < · · · < of positive integers for which xn xn +1 → 1. In this case we prove that the set G(Xn) of distribution functions of the sequence of blocks Xn = x x n 1 , x x n 2 , . . . , x x n n can be infinite. On the other hand if the ratio sequence xm , m = 1, 2, . . . , n, n = 1, 2, . . . is uniformly distributed, then xn → 1. xn xn+1
Keywords
Asymptotic distribution function, uniform distribution, ratio sequence, block.
Citation
Filip, F., Misık, L., & Toth, J. T. (2007). On distribution functions of certain block sequences. Uniform Distribution Theory, 2(1), 115–126.
F. Filip, L. Misık and J. T. Toth, “On distribution functions of certain block sequences,” Uniform Distribution Theory, vol. 2, no. 1, pp. 115–126, 2007.
Filip F, Misık L, Toth JT. On distribution functions of certain block sequences. Uniform Distribution Theory. 2007;2(1):115–126.
Filip, F., Misık, L. and Toth, J. T. (2007), ‘On distribution functions of certain block sequences’, Uniform Distribution Theory, 2(1), pp. 115–126.
Filip, Ferdinand, et al. “On Distribution Functions of Certain Block Sequences.” Uniform Distribution Theory, vol. 2, no. 1, 2007, pp. 115–126.
Filip, Ferdinand, Ladislav Misık, and Janos T. Toth. “On Distribution Functions of Certain Block Sequences.” Uniform Distribution Theory 2, no. 1 (2007): 115–126.
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Published by: Engineering Journals
