Confidence Region Radius

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.