Examples
Examples
Try the starting example
- Coordinate residuals [east,north]
- [[1,0],[-1,0],[0,2],[0,-2]]
- Bivariate normal coverage probability
- 0.95
- Sample mean east,north
- [0,0]
- Ellipse semimajor, semiminor, angle degrees
- [3.99715383646,1.99857691823,90]
- Horizontal RMS residual
- 1.581139
Try another scenario
- Coordinate residuals [east,north]
- [[1,0],[-1,0],[0,2],[0,-2]]
- Bivariate normal coverage probability
- 0.9
- Sample mean east,north
- [0,0]
- Ellipse semimajor, semiminor, angle degrees
- [3.5043478465,1.75217392325,90]
- Horizontal RMS residual
- 1.581139
Calculation method
Calculation method
Sample mean east,north
Arithmetic residual means.
Ellipse semimajor, semiminor, angle degrees
Sample covariance eigenvalues scaled by sqrt(−2ln(1−p)); normal-error assumption, not a confidence interval for the mean.
Horizontal RMS residual
sqrt(mean(east²+north²)).
Symbols and units
- a
- Coordinate residuals [east,north]
- b
- Bivariate normal coverage probability
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Coordinate residuals, confidence convention. Returns Covariance ellipse and summary errors. All coefficients and observations are user supplied; results describe only the stated mathematical model. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification. Bivariate normal coverage probability: minimum 1e-12, maximum 0.999999.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.