pingouin.madmedianrule(a)[source]

Robust outlier detection based on the MAD-median rule.

Parameters
aarray-like

Input array. Must be one-dimensional.

Returns
outliers: boolean (same shape as a)

Boolean array indicating whether each sample is an outlier (True) or not (False).

Notes

The MAD-median-rule ([1], [2]) will refer to declaring $$X_i$$ an outlier if

$\frac{\left | X_i - M \right |}{\text{MAD}_{\text{norm}}} > K,$

where $$M$$ is the median of $$X$$, $$\text{MAD}_{\text{norm}}$$ the normalized median absolute deviation of $$X$$, and $$K$$ is the square root of the .975 quantile of a $$X^2$$ distribution with one degree of freedom, which is roughly equal to 2.24.

References

1

Hall, P., Welsh, A.H., 1985. Limit theorems for the median deviation. Ann. Inst. Stat. Math. 37, 27–36. https://doi.org/10.1007/BF02481078

2

Wilcox, R. R. Introduction to Robust Estimation and Hypothesis Testing. (Academic Press, 2011).

Examples

>>> import pingouin as pg
>>> a = [-1.09, 1., 0.28, -1.51, -0.58, 6.61, -2.43, -0.43]