Joao P Dubas
5c044e69d9
1. The calculation made in `Grownth.Calc.Centile.compute/4` converts a given z-score into the expected measurement value. This can be used to get specific values for key z-scores, such as, -3, -2, 2 and 3. 2. To calculate the percentile of a given z-score the system uses the cumulative distribution function.
31 lines
867 B
Elixir
31 lines
867 B
Elixir
defmodule Growth.Calc.Percentile do
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@moduledoc """
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Convert the z-score of a given measurement into a cumulative percentile.
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This calculation is described in the [cumulative distribution function][https://en.wikipedia.org/wiki/Error_function#Cumulative_distribution_function].
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## Examples
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iex> z_scores = [-1.0, 0.0, 1.0]
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iex> Enum.map(z_scores, &apply(Growth.Calc.Percentile, :compute, :&1))
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[0.15865525393145707, 0.5, 0.8413447460685429]
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"""
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@doc """
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Convert the z-score of a given measurement into a percentile representation, ranging from 0 to 1.
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## Examples
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iex> Growth.Calc.Percentile.compute(2.0)
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0.9772498680518208
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iex> Growth.Calc.Percentile.compute(-2.0)
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0.02275013194817921
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"""
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@spec compute(number()) :: number()
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def compute(z_score) do
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0.5 * (:math.erf(z_score / :math.sqrt(2)) + 1)
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end
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end
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