Implements the TRUH test statistic for two sample testing under heterogeneity. TRUH incorporates the underlying heterogeneity and imbalance in the samples, and provides a conservative test for the composite null hypothesis that the two samples arise from the
same mixture distribution but may differ with respect to the mixing weights. See Trambak Banerjee, Bhaswar B. Bhattacharya, Gourab Mukherjee Ann. Appl. Stat. 14(4): 1777-1805 (December 2020).