| Bickel (1969) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
✔ |
✔ |
✖ |
✖ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
9 |
0 |
9 |
3 |
Comparison of CDFs, density or characteristic functions |
Comparison of CDFs |
NA |
| Biau and Gyorfi (2005) |
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✖ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
9 |
0 |
9 |
3 |
Comparison of CDFs, density or characteristic functions |
Comparison of CDFs |
NA |
| Boeckel, Spokoiny and Suvorikova (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Comparison of CDFs, density or characteristic functions |
Comparison of CDFs |
NA |
| Ntoutsi et al. (2008) |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
-- |
-- |
11 |
0 |
6 |
2 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Ganti et al. (1999) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
11 |
0 |
4 |
6 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Roederer et al. (2001) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✖ |
NA |
-- |
-- |
8 |
0 |
9 |
2 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Wang and Pei (2005) |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
NA |
-- |
-- |
9 |
0 |
8 |
2 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Ahmad and Cerrito (1993) |
✖ |
✔ |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
NA |
NA |
NA |
7 |
1 |
8 |
5 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Anderson, Hall and Titterington (1994) |
✖ |
✔ |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
NA |
9 |
1 |
8 |
3 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Cao and van Keilegom (2006) |
✖ |
✔ |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
✖ |
✖ |
✖ |
✖ |
✔ |
NA |
NA |
NA |
5 |
0 |
9 |
7 |
Comparison of CDFs, density or characteristic functions |
Comparison of density functions |
NA |
| Alba-Fernández, Ibáñez-Pérez and Jiménez-Gamero (2004) |
✖ |
✔ |
NA |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✖ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
7 |
0 |
8 |
6 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
| Alba Fernández, Jiménez Gamero and Muñoz García (2008) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✖ |
✖ |
✖ |
(✔) |
✔ |
NA |
✔ |
NA |
9 |
1 |
7 |
4 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
| Liu, Xia and Zhou (2015) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
✖ |
✖ |
✖ |
NA |
✔ |
NA |
NA |
NA |
5 |
0 |
9 |
7 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
| Li, Hu and Zhang (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
NA |
✔ |
NA |
10 |
0 |
4 |
7 |
Comparison of CDFs, density or characteristic functions |
Comparison of characteristic functions |
NA |
| Ghosh and Biswas (2016) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✖ |
✔ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
8 |
0 |
7 |
6 |
Rank-based |
Rank-based |
NA |
| Ghosal and Sen (2021) |
✖ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
5 |
9 |
Rank-based |
Rank-based |
R package testOTM |
| Deb, Bhattacharya and Sen (2021) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Rank-based |
Rank-based |
NA |
| Zhou and Chen (2023) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
7 |
3 |
6 |
5 |
Rank-based |
Rank-based |
NA |
| Engineer metric (Rachev, 1991) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✖ |
✔ |
✔ |
-- |
-- |
8 |
0 |
10 |
1 |
Discrepancy measure for distributions |
Probability metric |
NA |
| Zolotarev's (semi)metric (Rachev, 1991) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
✖ |
(✔) |
✔ |
✔ |
-- |
-- |
5 |
3 |
6 |
5 |
Discrepancy measure for distributions |
Probability metric |
NA |
| Ky Fan metric (Rachev, 1991) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
(✔) |
(✔) |
✖ |
✔ |
✔ |
✔ |
-- |
-- |
8 |
2 |
5 |
4 |
Discrepancy measure for distributions |
Probability metric |
NA |
| Prokhorov metric (Rachev, 1991) |
✖ |
✔ |
✖ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
7 |
0 |
5 |
7 |
Discrepancy measure for distributions |
Probability metric |
NA |
| Dudley metric |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
9 |
0 |
3 |
7 |
Discrepancy measure for distributions |
Probability metric |
NA |
| Total variation metric (Zolotarev, 1984) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
9 |
0 |
3 |
7 |
Discrepancy measure for distributions |
Probability metric |
NA |
| Kantorovich-Rubinstein metric (Zolotarev, 1984, Dudley, 1989) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
8 |
0 |
3 |
8 |
Discrepancy measure for distributions |
Probability metric |
NA |
| metric |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
7 |
0 |
4 |
8 |
Discrepancy measure for distributions |
Probability metric |
NA |
| q-Wasserstein metrics |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
✖ |
✔ |
✔ |
✔ |
-- |
-- |
9 |
2 |
7 |
1 |
Discrepancy measure for distributions |
Probability metric |
R package approxOT, transport |
| (Squared) Hellinger distance |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
(✔) |
-- |
-- |
9 |
1 |
3 |
6 |
Discrepancy measure for distributions |
Divergence |
R package abdiv |
| Vincze Le Cam distance (Vincze, 1981, Le Cam, 1986) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
(✔) |
-- |
-- |
8 |
1 |
3 |
7 |
Discrepancy measure for distributions |
Divergence |
NA |
| KL divergence (Kullback and Leibler, 1951) |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✖ |
✖ |
-- |
-- |
10 |
0 |
6 |
3 |
Discrepancy measure for distributions |
Divergence |
R package FNN |
| Jeffrey's divergence |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
✖ |
-- |
-- |
11 |
0 |
5 |
3 |
Discrepancy measure for distributions |
Divergence |
R package FNN |
| Extended divergence |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
NA |
NA |
NA |
✔ |
✔ |
(✔) |
-- |
-- |
8 |
1 |
4 |
6 |
Discrepancy measure for distributions |
Divergence |
NA |
| Jensen Shannon divergence |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
NA |
NA |
✔ |
✔ |
✔ |
(✔) |
-- |
-- |
10 |
1 |
3 |
5 |
Discrepancy measure for distributions |
Divergence |
R package philentropy |
| Pearson divergence (Pearson, 1900) |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
NA |
NA |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✖ |
✖ |
-- |
-- |
9 |
0 |
6 |
4 |
Discrepancy measure for distributions |
Divergence |
NA |
| Relative Pearson divergence (Yamada et al., 2013) |
✖ |
✔ |
✔ |
✔ |
NA |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✖ |
✖ |
-- |
-- |
7 |
0 |
6 |
6 |
Discrepancy measure for distributions |
Divergence |
NA |
| f-dissimilarity (García-García and Williamson, 2012, Györfi and Nemetz, 1975) |
✖ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
NA |
-- |
-- |
10 |
1 |
3 |
5 |
Discrepancy measure for distributions |
Divergence |
NA |
| Rényi divergence (Rényi, 1961) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
NA |
NA |
NA |
(✔) |
✖ |
✖ |
-- |
-- |
4 |
1 |
7 |
7 |
Discrepancy measure for distributions |
Divergence |
NA |
| Relative information of type s (Taneja and Kumar, 2004) |
✖ |
✔ |
✔ |
NA |
NA |
✖ |
NA |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✖ |
NA |
-- |
-- |
4 |
0 |
6 |
9 |
Discrepancy measure for distributions |
Divergence |
NA |
| H-divergence (Zhao et al., 2021) |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
(✔) |
(✔) |
NA |
NA |
NA |
6 |
2 |
5 |
8 |
Discrepancy measure for distributions |
Divergence |
NA |
| Muñoz et al. (2012) |
✖ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
-- |
-- |
6 |
0 |
7 |
6 |
Discrepancy measure for distributions |
Divergence |
NA |
| Muñoz, Martos and González (2013) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
-- |
-- |
7 |
0 |
7 |
5 |
Discrepancy measure for distributions |
Divergence |
NA |
| Friedman and Rafsky (1979) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
✖ |
14 |
0 |
6 |
1 |
Graph-based |
Graph-based |
R package gTests |
| Rosenbaum (2005) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
✔ |
|
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
NA |
14 |
0 |
5 |
2 |
Graph-based |
Graph-based |
R package crossmatch |
| Chen and Zhang (2013) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
|
✔ |
✔ |
✔ |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
9 |
0 |
6 |
3 |
Graph-based |
Graph-based |
R packages gTests, gCat |
| Biswas, Mukhopadhyay and Ghosh (2014) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
NA |
✔ |
13 |
0 |
5 |
3 |
Graph-based |
Graph-based |
R package LPKsample |
| Petrie (2016) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
|
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
13 |
0 |
4 |
4 |
Graph-based |
Graph-based |
R package multicross |
| Chen and Friedman (2017) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
12 |
0 |
5 |
4 |
Graph-based |
Graph-based |
R package gTests |
| Chen, Chen and Su (2018) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
13 |
0 |
5 |
3 |
Graph-based |
Graph-based |
NA |
| Zhang and Chen (2019) (weighted) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
9 |
0 |
6 |
3 |
Graph-based |
Graph-based |
R package gTests |
| Zhang and Chen (2019) (generalized) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
8 |
0 |
6 |
4 |
Graph-based |
Graph-based |
R package gTests |
| Zhang and Chen (2019) (max-type) |
✖ |
✖ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
NA |
NA |
-- |
-- |
-- |
✖ |
✔ |
NA |
NA |
NA |
7 |
0 |
6 |
5 |
Graph-based |
Graph-based |
R package gTests |
| Sarkar, Biswas and Ghosh (2020) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
(✔) |
✔ |
NA |
NA |
✔ |
NA |
NA |
✔ |
9 |
1 |
6 |
5 |
Graph-based |
Graph-based |
NA |
| Mukhopadhyay and Wang (2020) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
NA |
NA |
9 |
0 |
4 |
8 |
Graph-based |
Graph-based |
R package LPKsample |
| Mukherjee et al. (2022) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
14 |
0 |
3 |
4 |
Graph-based |
Graph-based |
R package multicross |
| Song and Chen (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
NA |
12 |
0 |
5 |
4 |
Graph-based |
Graph-based |
R package gTestsMulti |
| Weiss (1960) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✖ |
NA |
NA |
NA |
11 |
0 |
5 |
5 |
Graph-based |
Graph-based (NN) |
NA |
| Friedman and Steppel (1973) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
|
✖ |
NA |
NA |
✔ |
✔ |
✔ |
NA |
✖ |
NA |
✔ |
NA |
9 |
1 |
5 |
6 |
Graph-based |
Graph-based (NN) |
NA |
| Schilling (1986), Henze (1988) |
✖ |
✔ |
✖ |
✔ |
✔ |
(✔) |
✔ |
✖ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
✖ |
12 |
1 |
6 |
2 |
Graph-based |
Graph-based (NN) |
NA |
| Barakat, Quade and Salama (1996) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
NA |
NA |
11 |
0 |
6 |
4 |
Graph-based |
Graph-based (NN) |
NA |
| Nettleton and Banerjee (2001) |
✖ |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
-- |
NA |
✔ |
NA |
NA |
NA |
10 |
0 |
3 |
5 |
Graph-based |
Graph-based (NN) |
NA |
| Hall and Tajvidi (2002) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
10 |
0 |
6 |
5 |
Graph-based |
Graph-based (NN) |
NA |
| Chen, Dou and Qiao (2013) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✔ |
NA |
11 |
0 |
7 |
3 |
Graph-based |
Graph-based (NN) |
NA |
| Mondal, Biswas and Ghosh (2015) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
(✔) |
11 |
1 |
6 |
3 |
Graph-based |
Graph-based (NN) |
NA |
| Energy statistic (Zech and Aslan, 2003) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
|
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
(✔) |
14 |
1 |
6 |
0 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R package energy |
| Generalized energy statistic (Sejdinovic et al., 2013) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
(✔) |
✔ |
(✔) |
✔ |
NA |
10 |
2 |
7 |
2 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Chakraborty and Zhang (2021) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
(✔) |
✔ |
(✔) |
11 |
2 |
7 |
1 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| DISCO (Rizzo and Székely, 2010) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
✔ |
NA |
✔ |
NA |
11 |
0 |
7 |
3 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R package energy |
| Huang and Huo (2017) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
✖ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
NA |
NA |
7 |
0 |
10 |
4 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Deb and Sen (2021) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
|
✖ |
✔ |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
13 |
0 |
4 |
4 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R code on GitHub |
| Al-Labadi, Asl and Saberi (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
✔ |
NA |
10 |
0 |
5 |
6 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Baringhaus and Franz (2010) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
12 |
0 |
6 |
3 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
R package cramer |
| Liu and Modarres (2011) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
NA |
(✔) |
NA |
NA |
NA |
9 |
1 |
5 |
6 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Biswas and Ghosh (2014) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
✔ |
✔ |
13 |
0 |
5 |
3 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Sarkar and Ghosh (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
NA |
✔ |
9 |
0 |
6 |
6 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Montero-Manso and Vilar (2019) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
NA |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
✔ |
NA |
9 |
0 |
5 |
7 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| Tsukada (2019) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
NA |
NA |
✔ |
NA |
✔ |
✔ |
11 |
0 |
5 |
5 |
Comparison based on inter-point distances |
Comparison based on inter-point distances |
NA |
| MMD (Muandet et al., 2017, Gretton et al., 2009, , Gretton et al., 2012) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
✔ |
✔ |
✔ |
(✔) |
NA |
9 |
5 |
5 |
2 |
Kernel-based |
Kernel-based (MMD) |
NA |
| Block MMD (Zaremba et al., 2013) |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
✔ |
✔ |
✔ |
NA |
NA |
8 |
4 |
6 |
3 |
Kernel-based |
Kernel-based (MMD) |
matlab code on GitHub |
| fastMMD (Zhao and Meng, 2015) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
(✔) |
✔ |
(✔) |
✔ |
✔ |
✔ |
NA |
NA |
9 |
2 |
6 |
4 |
Kernel-based |
Kernel-based (MMD) |
NA |
| ME (Chwialkowski et al., 2015, Jitkrittum et al., 2016) |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
✔ |
✔ |
NA |
NA |
NA |
6 |
3 |
7 |
5 |
Kernel-based |
Kernel-based (MMD) |
python code on GitHub |
| SCF (Chwialkowski et al., 2015, Jitkrittum et al., 2016) |
✖ |
✔ |
NA |
✖ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
5 |
3 |
7 |
6 |
Kernel-based |
Kernel-based (MMD) |
python code on GitHub |
| regularized MMD (Danafar et al., 2014) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
|
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
7 |
4 |
4 |
6 |
Kernel-based |
Kernel-based (MMD) |
NA |
| Anisotropic kernel MMD (Cheng, Cloninger and Coifman, 2020) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
(✔) |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✔ |
NA |
✔ |
NA |
5 |
1 |
8 |
7 |
Kernel-based |
Kernel-based (MMD) |
NA |
| DMMD/ DFDA (Kirchler et al., 2020) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✖ |
✖ |
✔ |
|
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
8 |
3 |
6 |
4 |
Kernel-based |
Kernel-based (MMD) |
python code on GitHub |
| GPK (Song and Chen, 2023) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
8 |
3 |
5 |
5 |
Kernel-based |
Kernel-based (MMD) |
R package kerTests |
| Kernel FDA (Moulines, Bach and Harchaoui, 2007) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
(✔) |
NA |
✔ |
NA |
5 |
2 |
5 |
9 |
Kernel-based |
Kernel-based |
NA |
| Fromont et al. (2012) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
NA |
NA |
5 |
0 |
6 |
10 |
Kernel-based |
Kernel-based |
NA |
| Scetbon and Varoquaux (2019) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
(✔) |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
✖ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
✔ |
NA |
6 |
4 |
7 |
4 |
Kernel-based |
Kernel-based |
NA |
| Kernel-based quadratic distance (Chen and Markatou, 2020) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
7 |
3 |
5 |
6 |
Kernel-based |
Kernel-based |
NA |
| Bayesian kernel test (Zhang et al., 2022) |
✖ |
✔ |
(✔) |
✖ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
NA |
✔ |
NA |
NA |
NA |
7 |
1 |
7 |
6 |
Kernel-based |
Kernel-based |
NA |
| KMD (Huang & Sen, 2023) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
|
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
NA |
✔ |
NA |
16 |
0 |
3 |
2 |
Kernel-based |
Kernel-based |
R package KMD |
| Friedman (2004) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
(✔) |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
3 |
6 |
5 |
7 |
Method based on binary classification |
Method based on binary classification |
NA |
| C2ST (Lopez-Paz and Oquab, 2017) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
(✔) |
NA |
7 |
6 |
5 |
3 |
Method based on binary classification |
Method based on binary classification |
R package Ecume |
| Regression based test (Kim, Lee and Lei, 2019) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
NA |
✖ |
NA |
NA |
NA |
5 |
5 |
6 |
5 |
Method based on binary classification |
Method based on binary classification |
NA |
| Cheng and Cloninger (2022) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✖ |
✖ |
NA |
|
✖ |
✔ |
✖ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
NA |
NA |
5 |
3 |
8 |
5 |
Method based on binary classification |
Method based on binary classification |
NA |
| Yu et al. (2007) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
NA |
NA |
11 |
0 |
5 |
5 |
Method based on binary classification |
Method based on binary classification |
NA |
| DiProPerm test (Wei et al., 2016) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✖ |
NA |
(✔) |
NA |
5 |
5 |
6 |
5 |
Method based on binary classification |
Method based on binary classification |
R package diproperm |
| Classifier Probability Test (Cai, Goggin and Jiang, 2020) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
NA |
NA |
✖ |
NA |
NA |
(✔) |
(✔) |
(✔) |
NA |
✖ |
NA |
NA |
NA |
2 |
5 |
7 |
7 |
Method based on binary classification |
Method based on binary classification |
NA |
| Kim et al. (2021) |
✖ |
✔ |
(✔) |
✔ |
(✔) |
✖ |
✖ |
✖ |
✖ |
NA |
NA |
✔ |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
NA |
✔ |
NA |
(✔) |
(✔) |
6 |
7 |
5 |
3 |
Method based on binary classification |
Method based on binary classification |
NA |
| Hediger, Michel and Näf (2021) |
✖ |
✔ |
✔ |
(✔) |
✔ |
✖ |
(✔) |
✔ |
✖ |
✔ |
NA |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
NA |
✔ |
NA |
(✔) |
NA |
11 |
3 |
4 |
3 |
Method based on binary classification |
Method based on binary classification |
R package hypoRF |
| Feurer, Springenberg and Hutter (2015) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
(✔) |
NA |
NA |
NA |
NA |
✔ |
NA |
-- |
-- |
9 |
1 |
3 |
6 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
| Gromov-Hausdoff distance (Mémoli, 2017) |
✖ |
✔ |
(✔) |
NA |
NA |
✖ |
NA |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
-- |
-- |
5 |
1 |
5 |
8 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
| Leite, Brazdil and Vanschoren (2012), Leite and Brazdil (2021) |
✔ |
✔ |
✔ |
✔ |
(✔) |
✔ |
✔ |
✔ |
✖ |
NA |
NA |
(✔) |
✔ |
✔ |
(✔) |
(✔) |
(✔) |
✖ |
✔ |
✖ |
-- |
-- |
10 |
5 |
3 |
1 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
| DeDiMs (Calderon Ramirez et al., 2022) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✖ |
✖ |
NA |
NA |
6 |
0 |
8 |
7 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
NA |
| Alvarez-Melis and Fusi (2020) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
(✔) |
(✔) |
NA |
✔ |
✔ |
✔ |
-- |
-- |
11 |
2 |
4 |
2 |
Distance/ similarity measure for datasets |
Distance/ similarity measure for datasets |
python code on GitHub |
| DataSpheres (Johnson and Dasu, 1998) |
✖ |
✔ |
✔ |
✔ |
✖ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
NA |
NA |
6 |
0 |
5 |
10 |
Comparison based on summary statistics |
Comparison based on summary statistics |
NA |
| Constrained minimum distance (Tatti, 2007) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
-- |
-- |
8 |
0 |
6 |
5 |
Comparison based on summary statistics |
Comparison based on summary statistics |
NA |
| Romano (1989) |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
(✔) |
NA |
NA |
✔ |
NA |
✔ |
NA |
10 |
1 |
3 |
7 |
Testing approach |
Testing approach |
NA |
| Burke (2000) |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
✔ |
✖ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
✖ |
✖ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Testing approach |
Testing approach |
NA |
| Ping (2000) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
8 |
0 |
5 |
8 |
Testing approach |
Testing approach |
NA |
| Chen and Hanson (2014) |
✖ |
✔ |
✖ |
✔ |
NA |
✔ |
✔ |
✖ |
✖ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✔ |
✖ |
✔ |
NA |
7 |
0 |
7 |
7 |
Testing approach |
Testing approach |
NA |
| Zhou, Zheng and Zhang (2017) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✖ |
✖ |
NA |
(✔) |
(✔) |
5 |
2 |
8 |
6 |
Testing approach |
Testing approach |
NA |
| Pan et al. (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✖ |
✔ |
NA |
11 |
0 |
5 |
5 |
Testing approach |
Testing approach |
R package Ball |
| Wan, Liu and Deng (2018) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
NA |
✖ |
NA |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
5 |
9 |
Testing approach |
Testing approach |
NA |
| Kim, Balakrishnan and Wasserman (2020) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✖ |
✔ |
NA |
|
✖ |
✔ |
NA |
✔ |
NA |
NA |
✔ |
✔ |
NA |
✔ |
✔ |
11 |
0 |
5 |
5 |
Testing approach |
Testing approach |
NA |
| Li and Zhang (2020) |
✖ |
✔ |
✖ |
✔ |
✔ |
✖ |
✔ |
✔ |
✔ |
NA |
|
✖ |
✔ |
NA |
NA |
NA |
NA |
✔ |
✔ |
✔ |
✔ |
NA |
11 |
0 |
4 |
6 |
Testing approach |
Testing approach |
NA |
| Liu et al. (2022) |
✖ |
✔ |
✖ |
✔ |
✔ |
✔ |
✖ |
✖ |
✖ |
NA |
NA |
✖ |
✔ |
NA |
NA |
NA |
NA |
NA |
✔ |
NA |
✔ |
NA |
7 |
0 |
6 |
8 |
Testing approach |
Testing approach |
NA |
| Paul, De and Ghosh (2022a) |
✖ |
✔ |
(✔) |
✔ |
✔ |
✔ |
✔ |
✔ |
✖ |
✔ |
NA |
✖ |
✔ |
✔ |
(✔) |
(✔) |
NA |
NA |
✔ |
NA |
NA |
✔ |
11 |
3 |
3 |
4 |
Testing approach |
Testing approach |
R package HDLSSkST |