This paper presents a new likelihood-based partitioning method of the measurement set for the extended object probability hypothesis density (PHD) filter framework. Recent work has mostly relied on heuristic partitioning methods that cluster the measurement data based on a distance measure between the single measurements. This can lead to poor filter performance if the tracked extended objects are closely spaced. The proposed method called Stochastic Partitioning (StP) is based on sampling methods and was inspired by a former work of Granstrom et. al. In this work, the StP method is applied to a Gaussian inverse Wishart (GIW) PHD filter and compared to a second filter implementation that uses the heuristic Distance Partitioning (DP) method. The performance is evaluated in Monte Carlo simulations in a scenario where two objects approach each other. It is shown that the sampling based StP method leads to an improved filter performance compared to DP.