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Statistex.Robust

Statistex.Robust provides robust, range-based statistical methods built on top of the Statistex library.

Github repo: https://github.com/chazzka/statistex_robust

Installation

The package can be installed by adding statistex_robust to your list of dependencies in mix.exs:

def deps do
  [
    {:statistex_robust, "~> 0.1.0"}
  ]
end

Quickstart

For quickstart please refer to the test folder for simple examples or to the example folder for more robust examples on larger datasets.

Run with:

$ MIX_ENV=example mix run example/example_bootstrap.ex

Methods

medcouple/1

Calculates the medcouple, a robust statistic that measures skewness in a univariate distribution. Requires Rscript to be available in the shell path.

iex> Statistex.Robust.medcouple([1, 1, 1, 1, 1, 1])
0.0

iex> Statistex.Robust.medcouple([0, 2, 2, 2, 2, 5, 10])
0.4

medcouple/2

Calculates the medcouple for a specific column in a matrix.

iex> Statistex.Robust.medcouple([[1], [1], [1], [1], [1], [1]], 0)
0.0

adjusted_box/1

Calculates the adjusted boxplot bounds for a univariate dataset, considering the medcouple for skewness. Requires medcouple.

iex> Statistex.Robust.adjusted_box([1, 1, 1, 1, 1, 1])
{1.0, 1.0}

iex> Statistex.Robust.adjusted_box([0, 1, 2, 3, 4, 5])
{-4.5, 9.5}

adjusted_box/2

Calculates the adjusted boxplot bounds for a specified column (index) of a matrix.

iex> Statistex.Robust.adjusted_box([[1], [1], [1], [1], [1], [1]], 0)
{1.0, 1.0}

z_score/2

Estimates the range using Z-score for a univariate dataset.

iex> Statistex.Robust.z_score([39.0157, 50.9985, 45.1634, 63.6410, 48.1637, 54.4420, 56.6881, 49.0387, 51.9994, 45.2520], 3)
{29.837277543944065, 71.04322245605594}

z_score/3

Estimates the range using Z-score for a specified column (index) in a matrix.

iex> Statistex.Robust.z_score([[39.0157], [50.9985], [45.1634], [63.6410], [48.1637], [54.4420], [56.6881], [49.0387], [51.9994], [45.2520]], 3, 0)
{29.837277543944065, 71.04322245605594}

mad/2

Estimates range using the Median Absolute Deviation (MAD) for a univariate dataset.

iex> Statistex.Robust.mad([1, 2, 3, 4, 5, 6, 7], 3)
{-2.0, 10.0}

iex> Statistex.Robust.mad([10, 15, 20, 30, 50], 2)
{0.0, 40.0}

mad/3

Estimates range using the MAD for a specified column (index) in a matrix.

iex> Statistex.Robust.mad([[1], [2], [3], [4], [5], [6], [7]], 3, 0)
{-2.0, 10.0}

iex> Statistex.Robust.mad([[10], [15], [20], [30], [50]], 4, 0)
{-20.0, 60.0}

mad_skew/2

Calculates an asymmetric interval around the median using a skew-adjusted MAD.

iex> Statistex.Robust.mad_skew([1, 2, 3, 4, 5, 6, 7], 3)
{-0.5, 8.5}

iex> Statistex.Robust.mad_skew([10, 15, 20, 30, 50], 4)
{0.0, 60.0}

mad_skew/3

Calculates an asymmetric interval around the median using skew-adjusted MAD for a specific column (index) in a matrix.

iex> Statistex.Robust.mad_skew([[1], [2], [3], [4], [5], [6], [7]], 3, 0)
{-0.5, 8.5}

iex> Statistex.Robust.mad_skew([[10], [15], [20], [30], [50]], 2, 0)
{10.0, 40.0}

minmax/2

Calculates the minimum and maximum values for a specific column in a matrix.

iex> Statistex.Robust.minmax([[1, 2, 3], [4, 5, 6], [7, 8, 9]], 0)
{1, 7}

iex> Statistex.Robust.minmax([[10, 20], [5, 15], [25, 30]], 1)
{15, 30}

Statistex.Robust.Bootstrap

Provides a method for estimating the original data range from a sample using bootstrapping with extrapolation. This approach generates resampled data, calculates the min and max values for each resample, and applies a percentage-based extrapolation to estimate a wider range.

extrapolate/3

Performs bootstrapping with extrapolation to estimate a wider range for the original data based on the provided sample.

iex> data = [57, 57, 57, 58, 63, 66, 66, 67, 67, 68, 69, 70, 70, 70, 70, 72, 73, 75, 75, 76, 76, 78, 79, 81]
iex> n_resamples = 1000
iex> extrapolation_percentage = 0.10
iex> Statistex.Robust.Bootstrap.extrapolate(data, n_resamples, extrapolation_percentage)
{51.3, 89.1}

extrapolate/4

Estimates range using extrapolate/3 for a specified column (index) of a matrix.

iex> data = [[57], [58], [63], [66], [67], [68], [69], [70], [72], [73], [75], [76], [78], [79], [81]]
iex> Statistex.Robust.Bootstrap.extrapolate(data, 1000, 0.10, 0)
{51.3, 89.1}

The docs can be found at https://hexdocs.pm/statistex_robust.