Detecting outlier with combining two vectors
Autoencoder Solution

You could try an autoencoder. The autoencoder would take an input vector and it would try to recreate it as an output. So you take your input, and measure the distance between the input and the predicted output variable, using your metric of choice (euclidean should work but try various). Larger distances can be thought of as more abnormal. So you can stack rank your observations from weirdest to most normal.

Make sure that you are only training the autoencoder on normal data though. This would of course assume that you have more than the 13 samples that you are looking at. If not this probably isn't going to work very well, just because of the small sample.

KDE Solution

The idea is to use Kernel Density Estimation to generate a non-parametric joint density of your data set. You then find what the probability of finding a value that extreme would be. Here is some code using python's sklearn package:

from sklearn.neighbors.kde import KernelDensity
import numpy as np
X=np.matrix([[1.3269, 1.3354, 1.3318, 1.3282, 1.34666, 1.3460, 1.36084, 1.3526, 1.3539, 1.3510, 1.3480, 1.3479, 1.34893],[0.0352, 0.0992, 0.1570, 0.1431, 0.1634, 0.1629, 0.1046, 0.1655, 0.1635, 0.1642, 0.1658, 0.1666, 0.15735]])
kde = KernelDensity(kernel='gaussian', bandwidth=.45).fit(X.T)
score=kde.score_samples(X.T)
prob=np.exp(score)
print(prob/prob[6])


This code shows that the observations in the lowest probability density areas are observations 1,2 and 7. Of course this would work better with a larger sample, and you need to fuss with the bandwidth to calibrate it, but that this should do it.