190,259 research outputs found
Moment-Based Ellipticity Measurement as a Statistical Parameter Estimation Problem
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
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
This paper deals with sequences of random variables belonging to a fixed
chaos of order 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 and . The proof of this four
moments theorem is based on a number of new estimates for contraction norms.
Applications concern homogeneous sums and -statistics on the Poisson space
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