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Variance upper bounds and a probability inequality for discrete α-unimodality

100%

Ageel M. I.

Applicationes Mathematicae

2000

tom 27

nr 4

403-410

Variance upper bounds for discrete α-unimodal distributions defined on a finite support are established. These bounds depend on the support and the unimodality index α. They increase as the unimodality index α increases. More information about the underlying distributions yields tighter upper bounds for the variance. A parameter-free Bernstein-type upper bound is derived for the probability that the sum S of n independent and identically distributed discrete α-unimodal random variables exceeds its mean E(S) by a positive value nt. The bound for P{S-nμ ≥ nt} depends on the range of the summands, the sample size n, the unimodality index α and the positive number t.

Thinnest Covering of the Euclidean Plane with Incongruent Circles

88%

Dorninger D.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

40-46

In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits for the asserted bound can be gained.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Applicationes Mathematicae

1 Ageel M. I.

1 Dorninger D.

1 2017

1 2000

Wyniki wyszukiwania

Variance upper bounds and a probability inequality for discrete α-unimodality

Thinnest Covering of the Euclidean Plane with Incongruent Circles