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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.

Evaluating improvements of records

63%

Rychlik T.

Applicationes Mathematicae

1996-1997

tom 24

nr 3

315-324

We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.

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2 Applicationes Mathematicae

1 Ageel M. I.

1 Rychlik T.

1 2000

1 1997

Wyniki wyszukiwania

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

Evaluating improvements of records