679 research outputs found
Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator
AMS classifications: 62G20, 62G32;asymptotic normality;confidence intervals;Edgeworth expansions;extreme value index;Hill estimator;regular variation;tail index
Edgeworth Expansions for the Distribution Function of the Hill Estimator
We establish Edgeworth expansions for the distribution function of the centered and normalized Hill estimator for the positive extreme value index.estimation;variation;statistical distribution
Interacting electrons in polygonal quantum dots
The low-lying eigenstates of a system of two electrons confined within a
two-dimensional quantum dot with a hard polygonal boundary are obtained by
means of exact diagonalization. The transition from a weakly correlated charge
distribution for small dots to a strongly correlated "Wigner molecule" for
large dots is studied, and the behaviour at the crossover is determined. In
sufficiently large dots, a recently proposed mapping to an effective
charge-spin model is investigated, and is found to produce the correct ordering
of the energy levels and to give a good first approximation to the size of the
level spacings. We conclude that this approach is a valuable method to obtain
the low energy spectrum of few-electron quantum dots
Assessing Confidence Intervals for the Tail Index by Edgeworth Expansions for the Hill Estimator
AMS classifications: 62G20, 62G32;
On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics
On the relationship between the almost sure stability of weighted empirical distributions and sums of order statistics.
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