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Confidence intervals for average success probabilities

100%

Mattner L. , Tasto C.

Probability and Mathematical Statistics

2015

tom Vol. 35, Fasc. 2

301--312

We provide Buehler-optimal one-sided and valid two-sided confidence intervals for the average success probability of a possibly inhomogeneous fixed length Bernoulli chain, based on the number of observed successes. Contrary to some claims in the literature, the one-sided Clopper-Pearson intervals for the homogeneous case are not completely robust here, not even if applied to hypergeometric estimation problems.

$L^q$-spectrum of the Bernoulli convolution associated with the golden ratio

84%

Lau K.-S. , Ngai S.-M.

Studia Mathematica

1998

tom 131

nr 3

225-251

Based on a set of higher order self-similar identities for the Bernoulli convolution measure for (√5-1)/2 given by Strichartz et al., we derive a formula for the $L^q$-spectrum, q >0, of the measure. This formula is the first obtained in the case where the open set condition does not hold.