Difference between revisions of "Elliptic Error Probable"

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<p style="text-align:right"><B>Previous:</B> [[Precision Models]]</p>
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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.
 
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, <math>s_x^2, s_y^2</math> note that the confidence interval in one dimension uses <math>\chi^2</math> values with (''n'' - 1) degrees of freedom, and:
 
If we are going to make separate estimates of variance in each axis, <math>s_x^2, s_y^2</math> note that the confidence interval in one dimension uses <math>\chi^2</math> values with (''n'' - 1) degrees of freedom, and:
 
:&nbsp; <math>\sigma_x^2 \in \left[\, \frac{(n-1)s_x^2}{\chi_2^2}, \ \frac{(n-1)s_x^2}{\chi_1^2} \,\right]</math>
 
:&nbsp; <math>\sigma_x^2 \in \left[\, \frac{(n-1)s_x^2}{\chi_2^2}, \ \frac{(n-1)s_x^2}{\chi_1^2} \,\right]</math>

Revision as of 16:09, 22 April 2015

Previous: Precision Models

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:

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