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Confidence Intervals, Circles, and Spheres

Updated 17 Mar 2008

R = CRR(S) computes the radius of the mean-centered interval, circle, or sphere with 95% probability given S, which is either a vector of standard deviations or a covariance matrix from a multivariate normal distribution. If S is a real, symmetric, positive semidefinite matrix, CRR(S) is equivalent to CRR(SQRT(EIG(S))). Scalar S is treated as a standard deviation.

R = CRR(S,P) computes the confidence region radius with probability P instead of the default, which is 0.95.

R = CRR(S,P,TOL) uses a quadrature tolerance of TOL instead of the default, which is 1e-15. Larger values of TOL may result in fewer function evaluations and faster computation, but less accurate results. Use [] as a placeholder to obtain the default value of P.

R = CRR(S,P,TOL,M) performs a bootstrap validation with M normally distributed random samples of size 1e6. Use [] as a placeholder to obtain the default value of TOL.

R = CRR(S,P,TOL,[M N]) performs a bootstrap validation with M normally distributed random samples of size N.

### Cite As

Tom Davis (2020). Confidence Region Radius (https://www.mathworks.com/matlabcentral/fileexchange/10526-confidence-region-radius), MATLAB Central File Exchange. Retrieved .

Tom Davis

Hello, Doug

While ellipses and ellipsoids are most common, confidence regions may assume other shapes. CRR(S) returns the radius of the mean-centered circle or sphere that contains, on average, 95% of a normally distributed random sample with covariance matrix S.

Doug B

will this give me the elliptical confidence region or do I need to do the transformation myself? What is the meaning of a spherical confidence region if the distribution is elliptical?

##### MATLAB Release Compatibility
Created with R13
Compatible with any release
##### Platform Compatibility
Windows macOS Linux