Robust Estimation of Gaussian Distribution Parameters from Breakdown Tests Data on Air Insulation

The accurate estimation of Gaussian distribution parameters (location and scale) is of vital importance for the statistical approach to the insulation coordination of overhead lines. Small variations of such parameters can sometimes induce to sensitive variation on the value of risk of failure. One of the main problems on data obtained from dielectric strength tests is the possible presence of outliers that strongly influence the results of any estimator. Aim of this paper is to provide the best estimator among those considered in relation to the number and the location of outliers in a sample. Monte Carlo simulation has been used for the generation of Gauss distributed samples both not contaminated and contaminated with outliers. Then the performance of 29 different estimators for the location parameter and 25 for the scale parameter have been discussed with the aim to select the best estimator in each condition considered. In particular the analysis has been conducted on samples with coefficient of variation between 1% and 10%, typical of breakdown behaviour of air insulation