Abstract In low count-rate experiments Gaussian statistics is often not appropriate. An example of likelihood analysis applied to determine the Kr activity using data from a low background liquid scintillator is presented. Uncertainties and upper limits calculation is shown together with a goodness-of-fit based on Monte Carlo and on the Smirnov-Cramer-Von Mises test. The likelihood ratio method...

Robin J. DEELEY †, Joshua T. HORWOOD ‡, Raymond G. MCLENAGHAN † and Roman G. SMIRNOV § † Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada E-mail: [email protected], [email protected] ‡ Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 OWA, United Kingdom E-mail: jh423@ca...

Alexander Kurz, Tao Liu, Peter Marquard, Alexander V. Smirnov, Vladimir A. Smirnov, and Matthias Steinhauser Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany Deutsches Elektronen Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany Scientific Research Computing Center, Moscow State University, 119991, Moscow, Russia Skobeltsyn Inst...

An important problem in statistics is to obtain information about the form of the population from which the sample is drawn. Goodness of fit test is employed to determine how well the observed sample data "fits" some proposed model. The standard goodness of fit statistics are inappropriate when the parameters of the hypothesized distribution are estimated from the data used for the test. In thi...

Following Alday and Maldacena [1], we describe a string theory method to compute the strong coupling behavior of the scattering amplitudes of quarks and gluons in planar N = 2 super Yang-Mills theory in the probe approximation. Explicit predictions for these quantities can be constructed using the all-orders planar gluon scattering amplitudes of N = 4 super Yang-Mills due to Bern, Dixon and Smi...

We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0, 1] random variables stays to one side of a given line.

We study real Smirnov functions and investigate a certain ∗-closed subalgebra of the Smirnov class N+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space Hp ∩ Hp. This leads to a natural analog of the Riesz projection on a certain quotient space of Lp for p ∈ (0, 1). We also study a Herglotz-like integral transform for singular measures on ...

We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala's conjecture that the Hausdorff dimension of a $k$-quasicircle is