Peirce's Criterion for Outlier Rejection

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Apply Peirce's criterion for outlier detection for arbitrary number of observations 3 or more using Gould's implementation.

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Updated Thu, 04 Nov 2021 04:55:48 +0000

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Apply Peirce's criterion for outlier detection for arbitrary number of observations 3 or more. Gould's implementation of Peirce's method is used. This implementation doesn't use lookup tables unlike the other submission and computes the ratios using Gould's formulae. Hence the application is not limited to a particular number of observations.
Usage
Input DELTAS is a vector of the observations (or fit errors). Optional second input NUM_UNKNOWS is the number of "unknown quantities". Default value is 1 which is generally the case as argued by the authors. The function returns linear indices of outliers (OUTLIERINDICES), linear indices of observations which are found to be worthy of keeping (INLIERINDICES), and actual observations that are flagged as outliers.
Example
This example is from Peirce's original 1852 publication. Observations 1.01 and -1.4 are flagged as outliers.
z = [-0.3 0.48 0.63 -0.22 0.18 -0.44 -0.24 -0.13 -0.05 0.39 1.01 0.06 -1.4 0.2 0.1];
>> [outlierIdx,inlierIdx,outlierObs] = peirces(z)
outlierIdx =
11 13
inlierIdx =
1 2 3 4 5 6 7 8 9 10 12 14 15
outlierObs =
1.01 -1.4
References
B.A.Gould (1855), ON PEIRCE’S CRITERION FOR THE REJECTION OF DOUBTFUL OBSERVATIONS, WITH TABLES FOR FACILITATING ITS APPLICATION. The Astronomical Journal, No.83, Vol. IV.
B.PEIRCE (1852), CRITERION FOR THE REJECTION OF DOUBTFUL OBSERVATIONS. The Astronomical Journal, No.45, Vol. II.
S.M.ROSS, (2003) Peirce's criterion for the elimination of suspect experimental data. Journal of Engineering Technology.

Cite As

Chandrakanth R. Terupally, 2021. Peirce's Criterion for Outlier Rejection (https://www.mathworks.com/matlabcentral/fileexchange/<...>), MATLAB Central File Exchange. Retrieved November 3, 2021.

MATLAB Release Compatibility
Created with R2017a
Compatible with R2017a and later releases
Platform Compatibility
Windows macOS Linux

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