Elliptic Error Probable

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See section 2.3 of http://www.arl.army.mil/arlreports/2013/ARL-TR-6494.pdf for rectangular and elliptical statistics on asymmetric bivariate normal distributions.

If we are going to make separate estimates of variance in each axis, \(s_x^2, s_y^2\) note that the confidence interval in one dimension uses \(\chi^2\) values with (n - 1) degrees of freedom, and:

  \(\sigma_x^2 \in \left[\, \frac{(n-1)s_x^2}{\chi_2^2}, \ \frac{(n-1)s_x^2}{\chi_1^2} \,\right]\)