190,259 research outputs found

    Moment-Based Ellipticity Measurement as a Statistical Parameter Estimation Problem

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    We show that galaxy ellipticity estimation for weak gravitational lensing with unweighted image moments reduces to the problem of measuring a combination of the means of three independent normal random variables. Under very general assumptions, the intrinsic image moments of sources can be recovered from observations including effects such as the point-spread function and pixellation. Gaussian pixel noise turns these into three jointly normal random variables, the means of which are algebraically related to the ellipticity. We show that the random variables are approximately independent with known variances, and provide an algorithm for making them exactly independent. Once the framework is developed, we derive general properties of the ellipticity estimation problem, such as the signal-to-noise ratio, a generic form of an ellipticity estimator, and Cram\'er-Rao lower bounds for an unbiased estimator. We then derive the unbiased ellipticity estimator using unweighted image moments. We find that this unbiased estimator has a poorly behaved distribution and does not converge in practical applications, but demonstrates how to derive and understand the behaviour of new moment-based ellipticity estimators.Comment: 11 pages, 7 figures; v2 matches accepted version with minor change

    Probabilistic load flow in systems with high wind power penetration

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    This paper proposes a method for solving a probabilistic load flows that takes into account the uncertainties of wind generation, but also of load and conventional systems. The method uses a combination of methods including cumulant, point estimate and convolution. Cornish Fisher expansion series are also used to find the CDF. The method is of especial application to estimate active power flows through lines

    A four moments theorem for Gamma limits on a Poisson chaos

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    This paper deals with sequences of random variables belonging to a fixed chaos of order qq generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q=2q=2 and q=4q=4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and UU-statistics on the Poisson space
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