Abstract
In this paper a simple Gaussian approximation of the distribution of the weighted sum of squared normal variables is proposed. The proposed approximation is computationally less complex compared to other known approximations. However, the convergence towards Gaussian distribution is guaranteed provided the weights comply with certain limit conditions. The suggested approximation is applied to the calculation of confidence limits of the quadratic forms in normal variables. These problems can be encountered in a number of statistical decision making tasks. The accuracy of the estimated confidence limit is investigated on several simulation examples.
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