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A distance-based method to reconstruct a phylogenetic tree with $n$ leavestakes a distance matrix, $n \times n$ symmetric matrix with $0$s in thediagonal, as its input and reconstructs a tree with $n$ leaves using tools incombinatorics. A safety radius is a radius from a tree metric (a distancematrix realizing a true tree) within which the input distance matrices must alllie in order to satisfy a precise combinatorial condition under which thedistance-based method is guaranteed to return a correct tree. A stochasticsafety radius is a safety radius under which the distance-based method isguaranteed to return a correct tree within a certain probability. In this paperwe investigated stochastic safety radii for the neighbor-joining (NJ) methodand balanced minimal evolution (BME) method for $n = 5$.

Stochastic safety radius on Neighbor-Joining method and Balanced Minimal Evolution on small trees