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This paper summarizes the application of statistical algorithms for fault location on power transmission lines. The proposed fault location algorithms utilize statistical information about the undefined parameters such as equivalent impedances of the system at the unmonitored end of the transmission line, or those containing random errors. Knowledge about the distribution of these values results in more accurate fault location for lines with grounded neutral, especially in case of distant short circuits through a large transient resistance. The proposed algorithms are based on modelling of the faulted line and the Monte-Carlo method. The algorithms calculate not only the expected value of the distance to the fault, but also another important additional characteristic for the fault location, namely, the length of the line segment, where the short circuit could have occurred. The algorithm retains its applicability in cases of all the simple fault types and needs minor modifications for conditions when one breaker is opened and a single-phase fault is sustained.