```
set.seed(100)
d=200
vmu = rep(1.1/sqrt(d),d)
vsd = c(rep(1.1, d/5), rep(1, d-d/5))
num1 = 100
num2 = 100
s1 = matrix(0,num1,d) # sample 1
s2 = matrix(0,num2,d) # sample 2
for (i in 1:num1) {
s1[i,] = rnorm(d)
}
for (i in 1:(num2)) {
s2[i,] = rnorm(d, mean = vmu, sd = vsd)
}
num1 = nrow(s1) # number of observations in sample 1
num2 = nrow(s2) # number of observations in sample 2
```

The data of both samples have 200 variables. We take a look at the matrix of scatterplots of the first five variables for the two samples.

```
plot_dat = cbind(as.data.frame(rbind(s1[,1:5], s2[,1:5])), label = rep(c('sample 1', 'sample 2'), each = 100))
my_cols = c("#00AFBB", "#E7B800")
pairs(plot_dat[, 1:5], col = my_cols[as.factor(plot_dat$label)])
```

Even though we know the observations from two samples are generated from different distribution, it is hard to tell the differnce by looking at the scatterplots.

`res1 = rg.test(data.X = s1, data.Y = s2, n1 = num1, n2 = num2, k = 5, weigh.fun = weiMax, perm.num = 1000, progress_bar = F)`

type | test statistic | p value |
---|---|---|

robust generalized(asymptotic) | 9.00485158688115 | 0.0110820810661949 |

robust max-type(asymptotic) | 2.37080471135692 | 0.0264665891417283 |

robust generalized(permutation) | NA | 0.013 |

robust max-type(permutation) | NA | 0.022 |

```
data = rbind(s1, s2)
dist = dist(as.matrix(data))
res2 = rg.test(dis = dist, n1 = num1, n2 = num2, k = 5, weigh.fun = weiMax, perm.num = 1000)
```

type | test statistic | p value |
---|---|---|

robust generalized(asymptotic) | 9.00485158688115 | 0.0110820810661949 |

robust max-type(asymptotic) | 2.37080471135692 | 0.0264665891417283 |

robust generalized(permutation) | NA | 0.015 |

robust max-type(permutation) | NA | 0.026 |

```
E = kmst(dis=dist, k=5)
res3 = rg.test(E = E, n1 = num1, n2 = num2, weigh.fun = weiMax, perm.num = 1000)
```

type | test statistic | p value |
---|---|---|

robust generalized(asymptotic) | 9.00485158688115 | 0.0110820810661949 |

robust max-type(asymptotic) | 2.37080471135692 | 0.0264665891417283 |

robust generalized(permutation) | NA | 0.016 |

robust max-type(permutation) | NA | 0.032 |

The two-sample test is done. We can see the asymptotic results are the same by using the data matrices, the distance matrix or the edge matrix generated by 5-MST. The p-values based on the permutation method are similar to those based on asymptotic method.