Given a sample, the routine looks for outliers and gives back their indexes that identify them in the input vector.
The routine allows the specification of the critical probability (alpha, default is 0.01 = 1%), can manage NaNs and, as default, it uses statistics (biweight) that are robust to outliers because the sample mean and the standard deviation are not.
If requested a figure showing data values and outliers is also created.
Modified Thompson's Tau is recommended by Measurement Uncertainty (Part I, ASME PTC 19.1 1998) for the individuation of outliers in a set of repeated measurements.
As usual, suggested alpha goes from 0.1 (indicate all moderately suspicious outlier) to 0.01 (indicate only the bigger suspect values) or even smaller (allow even very big values and indicates only the huge ones).
To obtain the result you are looking for you can adjust alpha; otherwise, if data are expected to be very skewed, you must use another test or transform the data via a non-linear transformation.
The implemented version works with or without the statistic toolbox, but in the last case the value of alpha is fixed to the default value (0.01, 1%)
Additional specifications on the test and on the algorithm are given as comments in the code.
Michele Rienzner (2022). Find Outliers with Thompson Tau (https://www.mathworks.com/matlabcentral/fileexchange/27553-find-outliers-with-thompson-tau), MATLAB Central File Exchange. Retrieved .
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