isoutlier

bv = isoutlier(x; critic=3.0, method::Symbol=:median, threshold=nothing, width=0.0) -> Union{BitVector, BitMatrix}

Return a logical array whose elements are true when an outlier is detected in the corresponding element of x.

If x is a matrix, and width is not used, then isoutlier operates on each column of x separately. By default, an outlier is a value that is more than three median absolute deviations (MAD) from the median. But that can be changed via the critic option.

critic: A number that sets the threshold for detecting outliers. The default is 3.0, which means that a value is considered an outlier if it is more than 3 MAD from the median (when method is :median), or more than 3 standard deviations (when method is :mean).
method: The method used to calculate the threshold for outliers. It can be one of the following:
- median: Uses the median absolute deviation (MAD) method. Outliers are defined as elements more than critic MAD from the median.
- mean: Uses the mean and standard deviation method. Outliers are defined as elements more than critic standard deviations from the mean. This method is faster but less robust than “median”.
- quartiles: Uses the interquartile range (IQR) method. Outliers are defined as elements more than 1.5 interquartile ranges above the upper quartile (75 percent) or below the lower quartile (25 percent). This method is useful when the data in x is not normally distributed.
threshold: Is an alternative to the method option. It specifies the percentile thresholds, given as a two-element array whose elements are in the interval [0, 100]. The first element indicates the lower percentile threshold, and the second element indicates the upper percentile threshold. It can also be a single number between (0, 100), which is interpreted as the percentage of end member points that are considered outliers. For example, threshold=1 means that the lower and upper thresholds are the 1th and 99th percentiles.
width: If this option is used (only when x is a Matrix or a GMTdataset) we detect local outliers using a moving window method with window length width. This length is given in the same units as the input data stored in first column of x.

Examples

x = [57, 59, 60, 100, 59, 58, 57, 58, 300, 61, 62, 60, 62, 58, 57];
findall(isoutlier(x))
2-element Vector{Int64}:
 4
 9

x = -50.0:50;   y = x / 50 .+ 3 .+ 0.25 * rand(length(x));
y[[30,50,60]] = [4,-3,6];   # Add 3 outliers
findall(isoutlier([x y], width=9))

Source Code

This function has multiple methods: