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Confidence Region Radius

26 Mar 2006 (Updated 17 Mar 2008)

Confidence Intervals, Circles, and Spheres

File Information
Description	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.
Acknowledgements	The author wishes to acknowledge the following in the creation of this submission: SEP - An Algorithm for Converting Covariance to Spherical Error Probable This submission has inspired the following: Rectangular Confidence Regions
MATLAB release	MATLAB 6.5 (R13)
Zip File Content
Other Files	crr.pdf, crr.m

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Everyone's Tags	cep, multivariate normal distribution, pe, probability, sep, statistics
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Updates
30 Mar 2006	minor revisions
31 Mar 2006	added screenshot
19 Apr 2006	minor revisions
24 Apr 2006	added erf of pure imaginary argument
11 May 2006	performance and accuracy enhancements for extreme values
17 May 2006	introduced central binomial coefficients and incomplete gamma function
26 May 2006	added quadrature tolerance and changed parameter order; added asymptotic erf expansion; enhanced documentation.
06 Jun 2006	minor revisions
13 Jun 2006	added Newton's method
27 Jun 2006	added covariance matrix input
05 Jul 2006	allow zero variances
02 Oct 2006	minor revisions
27 Oct 2006	description spelling correction
17 Mar 2008	updated contact information

Tag Activity for this File
Tag	Applied By	Date/Time
statistics	Tom Davis	22 Oct 2008 08:20:27
probability	Tom Davis	22 Oct 2008 08:20:27
sep	Tom Davis	22 Oct 2008 08:20:28
multivariate normal distribution	Tom Davis	22 Oct 2008 08:20:28
cep	Tom Davis	22 Oct 2008 08:20:28
pe	Tom Davis	22 Oct 2008 08:20:28

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