Ellipse mean radius: most accurate estimation

Asked Jan 15 '20 at 02:09

Active Jan 15 '20 at 02:17

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What would be the most accurate estimation of the mean/average radius of an elliptic distribution with radii: semi-major axis rmax and semi-minor axis rmin among these? Are there others?

r_mean = sqrt((rmax^2 + rmin^2)/2)
r_mean = (2*rmax + rmin)/3
r_mean = sqrt(rmax + rmin)

The distribution arises from two independent variables U and V: when represented in 2D space they yield an elliptic shape.

edited Jan 15 '20 at 02:17

asked Jan 15 '20 at 02:09

slkuser

Perhaps include a reference for "elliptic distribution". – GEdgar Jan 15 '20 at 02:12
Equating the area of an ellipse to that of a circle of radius equivalent to the average radius gives you the geometric mean of the semi minor and major axes – Dhanvi Sreenivasan Jan 15 '20 at 02:25
"Most accurate" with respect to what? – Intelligenti pauca Jan 15 '20 at 17:47
Please refer to my answers for other posts at here and here. – Ng Chung Tak Jan 15 '20 at 20:07
@Tak: many thanks. I am more inclined accept the angular average method, given sounder mathematical rationale/robustness. I tested it against 1 and 3 and all three are consistent. Can you please post it to close this question. – slkuser Jan 16 '20 at 00:35

Ellipse mean radius: most accurate estimation

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